Cube (algebra)

$y = x 3$ for values of $1 \leq x \leq 25$ .

In arithmetic and algebra, the cube of a number $n$ is its third power, that is, the result of multiplying three instances of $n$ together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2³ = 8 or $(x + 1) 3$ .

The cube is also the number multiplied by its square:

n 3 = n \times n 2 = n \times n \times n

.

The cube function is the function $x \mapsto x 3$ (often denoted $y = x 3$ ) that maps a number to its cube. It is an odd function, as

(- n) 3 = -(n 3)

.

The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists 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.

The graph of the cube function is known as the cubic parabola. Because the cube function is an odd function, this curve has a center of symmetry at the origin, but no axis of symmetry.