In arithmetic and algebra, the **cube** of a number *n* is its third power — the result of multiplying it by itself two times: *n*^{3} = *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 = 2
^{3} + 2^{3} + 1^{3} + 1^{3} + 1^{3} + 1^{3} + 1^{3} + 1^{3} + 1^{3} Each cube number *n*^{3} is also the sum of the first *n* centered hexagonal numbers, although representing a different shape. |