The volume of a cube is calculated by multiplying the side length, $s,$ with itself $3$ times: $$V=s\cdot s\cdot s\iff V=s^3.$$ This stems from the fact that the volume of all rectangular prisms is calculated by multiplying the area of the base, $B,$ and the height, $h.$

The height will be of length $s$ and the volume can be expressed as: $$V=B\cdot s$$ Since the base of a cube is a square, its area is calculated by multiplying two sides. Therefore, $B$ can be replaced with $s\cdot s$: $$V=s\cdot s\cdot s\iff V=s^3.$$