The cube of a number $x$ is the third power $x^3$ of $x$ Similarly one may speak of the cube of an element $x$ in any semigroup with the operation denoted multiplicatively (cf. general associativity).

The volume of a cube (i.e. regular hexahedron) with edge length $a$ is $a^3$ hence the name.

The cube function $x\mapsto x^3$ , from $\mathbb{R}$ to $\mathbb{R}$ is injective, but not as a mapping from $\mathbb{C}$ to $\mathbb{C}$ one has $x^3 = y^3$ , always when $\frac{x}{y} = \frac{-1\pm i\sqrt{3}}{2}$ the primitive third root of unity.