How to find cube of a number

Find the cubed value of a number n. Enter positive or negative whole numbers or decimal numbers or scientific E notation.

Cubing Negative Numbers

When you cube negative numbers the answer will always be negative. In this calculator you do not need to use parentheses with your input because you will still get the correct answer although, you should be aware that below is how your inputs are actually interpreted by the calculator.

• -2³ means -(2 × 2 × 2) = -8
• -(2)³ means -(2 × 2 × 2) = -8
• (-2)³ means (-2 × -2 × -2) = -8

When an exponent expression is written with a positive value such a 4³ it is easy for most anyone to understand this means 4 × 4 × 4 = 64

However, when the value to be operated on by the exponent is written as a negative value without parentheses the meaning is ambiguous. It has a different meaning to different people.

Different possible interpretations of -4³:

1. negative of (4 cubed) or -(4)³ = -(4 × 4 × 4) = -64

2. (negative 4) cubed or (-4)³ = (-4 × -4 × -4) = -64

Use parentheses to clearly indicate which calculation you really want to happen. Parentheses don't change your results when the exponent is odd like a 3 but it makes a clear difference when your exponent is even like a 2. Square Calculator for -4²

Cube numbers can be a little bit more confusing than squared numbers, simply because of the extra multiplication. Essentially, you are calculating a 3D shape instead of a flat one.

Here is a flat (or 2D) 4 x 4 square:

To calculate the number of blocks (the squared number) we would simply multiply 4 x 4 or 42, equalling 16.

Here is a 3D 4 x 4 cube:

To calculate the number of blocks (the cubed number) this time we would multiply 4 x 4 x 4 or 43 equalling 64.

In KS2, you won’t need to learn cube numbers off by heart, but you will have to have a basic understanding of what they are, and how to calculate them. Often children will be given a pattern of numbers, such as lower end cube numbers and may be asked to try to work out the pattern.

Here is a list of cubed numbers up to 12x12:

The cube of a negative number will always be negative, just like the cube of a positive number will always be positive.

For example; -53 = -5 x -5 x- -5 = (25 x -5) = -125.

Just like whole numbers (integers), it’s easy to cube a decimal number too. Don’t worry though, you won’t need to memorise these in key stage 2 (or probably even work them out)!

Here are some worksheets aimed specifically at getting to grips with cube numbers and practising your skills.

Year 6 – Drawing dice dots on net cubes

Year 8 – Know your squares and your cubes

Year 8 – Cube numbers and cube roots

Year 8 – Practise finding cubes and cube roots on a calculator

If cube numbers and puzzles are your thing and you really want to give yourself a challenge, why not look at the BBC Bitesize website or try some of the puzzles and problems set by the NRich team at the University of Cambridge?

Candidates who are preparing for competitive exams should remember tables up to 30, squares, and cubes up to 20. This makes your calculation easier as well as quicker. Now, let's have a look at cubes up to 20.

You can practice questions asked in Bank exams with the Bank Test Series designed by the experts of BYJU'S Exam Prep.

Now, let`s have a look at the trick to solve the cubes.

We all know, to solve the cube of a number, we use the formula (a + b)3 which is a3 + 3a2b + 3ab2 + b3. 

Now, we will be using this method only but in a smart way so that you can find out the cube in cubes can be solved in exams in just a few seconds and without writing all the steps. So, you have to do the complete calculation in a single go.

I: Think the above formulae as a3 | 3a2b | 3ab2 | b3. We have divided the formulae into four parts. 

II: Then just calculate all these four parts and write their values.

III: Now, keep only one rightmost digit in each part from the right side and carry forward the extra digits to the previous left parts.

Let's have a look at some examples following the above steps for better understanding:

1. (23)3 :

I:   23 | 3. 22 . 3 | 3. 2 . 32 | 33 

II:  8  |     36     |      54     | 27

III:= 12      41             56       27                     

(Kept rightmost digit of each part from the right-hand side and Carry forward extra digits to the previous left part) 

Start from the right side,

In 27; 7 will be written and 2 will be carried 54.

Then 54 + 2 = 56. Now, 6 will be written and 5 carry forward to 36.

It will be 36 + 5 equals 41. Again, 1 will be written and 4 will be carried forward.

Finally, 8 + 4 is 12. Combining all, the cube of 23 is 12167.

Answer: 12167

2. (68)3 :

I:   63    | 3. 62 . 8 | 3. 6 . 82 | 83 

II:  216  |    864     |    1152  | 512

III:= 314          984            1203     512                 

(Kept rightmost digit of each part from the right-hand side and Carried forward extra digits to the previous left part) 

Start from the right side, in 512; 2 will be written and 51 will be carried 1152.

Then 1152 + 51 = 1203. Now, 3 will be written and 120 carry forward to the 864.

It will be 864 + 120 equals 984. Again, 4 will be written and 98 will be carried forward.

Finally, 216 + 98 is 314. Combining all, the cube of 68 is 314432.

Answer: 314432

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3. (109)3 :

I:   103    | 3. 102 . 9 | 3. 10 . 92 | 93 

II:  1000  |   2700     |    2430    | 729

III:=1295     2950          2502       729               

(Kept rightmost digit of each part from the right-hand side and Carried forward extra digits to the previous left part) 

Start from the right side, in 729; 9 will be written and 72 will be carried to 2430.

Then 2430 + 72 = 2502. Now, 2 will be written and 250 carry forward to 2700.

It will be 2700 + 250 equals 2950. Again, 0 will be written and 295 will be carried forward.

Finally, 1000 + 295 is 1295. Combining all, the cube of 68 is 1295029.

Answer: 1295029

By breaking the formula and solving it in parts make your calculation easier. Don`t forget to add carry forwarded values.

Let`s have a look at another way of using the formulae and another trick to solve the cubes

I: Write the numbers in the form of a3 | a2b | ab2 | b3

II: Calculate above values

II: Double (Multiply by 2) the second and third part from any of the sides.

III:  Now, adding the result of both the steps, write the final answer keeping only one digit at each part starting from the right-hand side.

Example: (64)3

I:   63  | 62 . 4 | 6 . 42 | 43 

II: 216| 144    |  96     | 64

III:     | 288    | 192    |        (144 and 96 are multiplied by 2) 

IV: 262   461     294        64  (Added II and III Steps)

In the above example, start from the right hand side, 4 is written and 6 is carried to (96 + 192 = 288).

Then 288 + 6 carry = 294. Now, 4 will be written and 29 is again carried to (144 + 288 = 442).

Then 442 + 29 carry = 461. Now, 1 will be written and 46 will be added to 216.

Then 216 + 46 equal to 262. Combining all cube of 64 is 262144.

Answer: 262144

Example:  (112)3

I:   113  | 112 . 2 | 11 . 22 | 23 

II: 1331|     242  |     44    | 8

III:             484  |     88        (242 and 44 are multiplied by 2)

IV:    1404  739       132      8 (Added II and III Steps)

Start from the right-hand side, 8 is a single digit so it is written.

Then in (44 +88) = 132, 2 will be written and 13 will be carry forward to previous part i.e, (242 +484) equals 726.

Now, 726 + 13 carry = 739. After that 9 is written and 73 carry forward to 1331

1331 +73 equal to 1404.  Combining all cube of 112 is 1404928.

Answer: 1404928  

Example:  (98)3

I:   93   | 92 . 8 | 9 . 82 | 83 

II:  729|  648   |  576   | 512

III:        1296  | 1152            (648 and 576 multiplied by 2)

IV: 941   2121   1779      512  (Added II and III Steps)

Start from the right-hand side, in 512, 2 is written and 51 carry forward to (576 + 1152 = 1728)

Then 1728 + 51 carry equals 1779. Now 2 is written and 177 carry forward to (648 + 1296 = 1944)

Then 1944 + 177 carry = 2121. Again only digit i., 1 is written and 212 is carried forward.

Finally, 212 + 729 is equal to 941. 

Combining all cube of 98 is 941192.

Answer: 941192 

Calculate the values of cubes of the numbers using these tricks easily. Make sure that you don't write all the steps in the exam. Just calculate the steps in your mind and answer it quickly.

Solve the following cubes and post your answer in the comment section:

1. (218)3 

2. (77)3

3. (111)3

4. (305)3

5. (83)3

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