Perfect Cube Calculator

Created by Madhu Raman
Reviewed by Wojciech Sas, PhD and Steven Wooding
Last updated: Nov 01, 2022

Are you searching for a quick tool that helps you identify if a number is a perfect cube? Look no further! Our perfect cube calculator will tell you if we can write a given number as the cube of an integer or not! Read on to know what a perfect cube is, how to find a perfect cube, and a list of some perfect cubes!

A cube is generally any number obtained by raising a given number to the power of 3. An interesting application of this concept lies in finding the volume of a cube.

Perfect cube definition

A perfect cube number is the number that results by raising an integer to the power of 3.

In other words, if we multiply an integer by itself three times, we get a perfect cube!

So mathematically, the following is the perfect cube formula:

A number NN is a perfect cube if we can write it as:

N=aβˆ—aβˆ—aN = a * a * a,

where aa is an integer.

Generally, if we can find what the cube root of a number is, and if that is an integer, our number will be a perfect cube!

How do we use the perfect cube calculator?

If you want to find out if a number NN is a perfect cube or not, simply key in its value into the Number field of the calculator!

The perfect cube calculator will then tell you if the number is a perfect cube, and if yes, you will also be able to see its cube root!

Which numbers are perfect cubes?

Here are some examples of perfect cubes:

  • 23=2Γ—2Γ—2=8\small 2^3 = 2 \times 2 \times 2 = 8, so 8\small 8 is a perfect cube!

  • Similarly, (βˆ’2)3 ⁣= ⁣(βˆ’2) ⁣× ⁣(βˆ’2) ⁣× ⁣(βˆ’2) ⁣=β€‰β£βˆ’8\small (-2)^3\! =\! (-2)\! \times\! (-2)\! \times\! (-2)\! =\! -8, so βˆ’8\small -8 is also a perfect cube!

  • 63=6Γ—6Γ—6=216\small 6^3 = 6 \times 6 \times 6 = 216, so 216\small 216 is a perfect cube!

  • Similarly, (βˆ’6)3 ⁣= ⁣(βˆ’6) ⁣× ⁣(βˆ’6) ⁣× ⁣(βˆ’6) ⁣=β€‰β£βˆ’216\small (-6)^3\! =\! (-6)\! \times\! (-6)\! \times\! (-6)\! =\! -216, so βˆ’216\small -216 is also a perfect cube!

Unlike square root, we can find cube roots for negative numbers too!

Some other examples of identifying perfect cubes are:

  • Given the number 100\small 100, its cube root is approximately 4.64\small 4.64, which is not an integer. So 100\small 100 is not a perfect cube.

  • Given the number βˆ’1000\small -1000, its cube root is βˆ’10\small -10, which is an integer. So βˆ’1000\small -1000 is a perfect cube number, which you can also check by using our perfect cube calculator!

  • Given the number 125,000\small 125,000, its cube root is 50\small 50, which is an integer. So, 125,000\small 125,000 is a perfect cube number which you can also verify using our perfect cube calculator!

List of Perfect Cubes

Here's a list of the first 10 perfect cubes for ready-reference:

Number

Cube of number

1

1

2

8

3

27

4

64

5

125

6

216

7

343

8

512

9

729

10

1000

Similar to perfect cubes, we also have perfect squares, which are numbers whose square roots are integers. Learn more about that in our perfect square calculator.

A few interesting extensions of the concept of roots, in general, are also available in the following tools:

Hey! We thought that instead of perfect cubes, you might be looking for magic squares: go to our magic square calculator and learn everything about them!

FAQ

Can the cube root of a number be negative?

Yes! The cube root of any negative number will always be negative, and the cube root of any positive number will always be positive.

Is 125 a perfect cube?

Yes! We can write 125 as 5 Γ— 5 Γ— 5, which means that the cube root of 125 is 5.

Since 5 is an integer, 125 is a perfect cube πŸŽ‰!

Is 64 a perfect cube?

Yes! We can write 64 as 4 Γ— 4 Γ— 4, which means that the cube root of 64 is 4.

Since 4 is an integer, 64 is a perfect cube πŸŽ‰!

Is 27 a perfect cube?

Yes! We can write 27 as 3 Γ— 3 Γ— 3, which means that the cube root of 27 is 3.

Since 3 is an integer, 27 is a perfect cube πŸŽ‰!

Is 8 a perfect cube?

Yes! We can write 8 as 2 Γ— 2 Γ— 2, which means that the cube root of 8 is 2.

Since 2 is an integer, 8 is a perfect cube πŸŽ‰!

Is 1 a perfect cube?

Yes! We can write 1 as 1 Γ— 1 Γ— 1, which means that the cube root of 1 is 1 itself.

So 1 is a perfect cube πŸŽ‰!

Is 0 a perfect cube?

Yes! We can write 0 as 0 Γ— 0 Γ— 0, which means that the cube root of 0 is 0 itself.

So 0 is a perfect cube πŸŽ‰!

Madhu Raman
Number
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