Cube (algebra)

In arithmetic and algebra, the cube of a number n is its third power: the result of the number multiplied by itself twice:

It is also the number multiplied by its square:

This is also the volume formula for a geometric cube with sides of length n, giving rise to the name. The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power.

Both cube and cube root are odd functions:

The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2³ = 8 or (x + 1)³.

In integers

A cube number, or a perfect cube, or sometimes just a cube, is a number which is the cube of an integer. The positive perfect cubes up to 60³ are (sequence A000578 in OEIS):

Geometrically speaking, a positive number m is a perfect cube if and only if one can arrange m solid unit cubes into a larger, solid cube. For example, 27 small cubes can be arranged into one larger one with the appearance of a Rubik's Cube, since 3 × 3 × 3 = 27.