Cube Numbers

In this article we are going to discuss cube numbers.

A couple of lines down you can find our calculator which can cube any real number.

The terms cube number and perfect cube are synonym.

It’s called perfect cube because the number is the cube of a whole number.

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Cube Numbers Definition

A perfect cube is the product of some integer with itself two times.

Therefore, it is expressed as n³ = n × n × n; n is a whole number.

As you can see, a cube number is an exponentiation involving the base n and the exponent 3, sometimes written as n^3.

In other words, it means n to the power of 3.

It follows from that that n can be positive or negative (if you cube a negative number the result will be a negative), but usually the meaning is n > 0.

If n represents the length of a side, then n^3 expresses the volume of the shape of a cube with side length n.

This answers the question how do you cube a number?

Cube Numbers Formula

n³ = n × n²

For n² you may use .

Next, let’s look at some examples.

Cube Numbers Examples

• Example 1 – 3: 3³ = 3 × 3 × 3 = 27.
• Example 2 – 4: 4³ = 4 × 4 × 4 = 64.
• Example 3 – 10: 10³ = 10 × 10 × 10 = 1000.

If n³ is the cube number, then n is the principal cube root.

• Example 4: The cube root of 1728 (12 × 12 × 12 = 12³ =) is 12.

To find out if a given integer is a perfect cube, calculate its cube roots.

If the cube root is a natural number (has no decimal places and is non-negative), then the number is indeed a cube number.

• Example 5: Is 224 a cube number? No, ∛224 = 6.0731779437 (has decimals).
• Example 6: Is 216 a cube number? Yes, ∛216 = 6 (has no decimals).
• Example 7: If the cube of a number is y, then what is the original number x? By definition, the product y = x³, so x = ∛y.

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If something remains unclear do not hesitate getting in touch with us.

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Ahead is the table in the context of this site.

Cube Numbers List

The table below answers the question what are the cube numbers from 1 to 100?

As follows, the sequence of perfect cubes is 0 (0 x 0 x 0), 1 (1 x 1 x 1), 8 (2 x 2 x 2), 27 (3 x 3 x 3), 64 (4 x 4 x 4), 125 (5 x 5 x 5), 216 (6 x 6 x 6), 343 (7 x 7 x 7), 512 (8 x 8 x 8), 729 (9 x 9 x 9), …

About our Cube Numbers Calculator

Here we would like to tell you that our tool at the top of this page works both ways; you can either fill in the top or the bottom input field.

Our app works with all real numbers, and you don’t need to press a button unless you want to go back to square one.

You may use the down and up arrows (called spinners) to decrease and increase the input value.

Frequently calculated terms on our site include, for instance:

• Cube of 9
• Cube Number of 1
• Cube Number of 26

We now provide you with some additional information regarding the shape, or which might be useful to you to come up with n^3.

Additional Information

A cube is a three-dimensional object: In geometry, it is the only regular hexahedron; it has 6 faces, 8 vertices and 12 edges.

n × n × n = length × width × height.

This is the difference between two perfect cubes:

(n + 1)³ − n³ = 3(n + 1)n + 1 ⇔ n³ − (n − 1)³ = 3(n − 1)n + 1.

The following symmetry applies:
(−n)³ = −(n³).

Note that you can always employ the search form located in the menu and in the sidebar of this site to locate information about a particular term.

Or simply consult our chart.

Next is the summary of our article.

Bottom Line

A cube number n³ means n × n × n, n is an integer and × is the multiplication symbol.

The exponentiation form n³ or n^3 is mostly used to express a cube.

If the third root of a cubed number has no decimal places, then the cubed number is a cube number!

If this article about the cube of numbers has been of help to you, then please share it by means of the social buttons below.

Perhaps you are also interested in the similar concept of square numbers which you can find here.

And should you want to give us feedback use the form at the bottom.

Resources related to squares and similar geometrical shapes can be found under “recommended sites” section in the sidebar.

Finally, don’t forget to install our absolutely free PWA app (see menu or sidebar), or to bookmark us.

And come back soon, practice makes perfect!

Thanks for your visit.

Further references:

• Cube eon Wikipedia

– Article written by Mark, last updated on November 26th, 2023

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