In arithmetic and algebra, the cube of a number n is its third power — the result of multiplying it by itself two times:

n³ = n × n × n.

This is also the volume formula for a geometric cube of side length n, giving rise to the name.

The term cube or cube number is often used to refer to a perfect cube i.e. a number that is the cube of a positive integer.

The series of perfect cubes starts as follows:

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, ...

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.

Every positive integer can be written as the sum of nine cubes or fewer; see Waring's problem. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine cubes :-

23 = 2³ + 2³ + 1³ + 1³ + 1³ + 1³ + 1³ + 1³ + 1³

Each cube number n³ is also the sum of the first n centered hexagonal numbers, although representing a different shape.