Answer
$S(V)=6V^{\frac{2}{3}}$, $V>0$
Work Step by Step
We know that the volume of a cube of side $x$ is:
$V=x^3$
And the surface area is:
$S=6x^2$
We solve for $x$ in the volume formula:
$V=x^3$
$x=\sqrt[3]{V}=V^{1/3}$
And plug into the surface area formula:
$S=6x^2$
$S=6(V^{\frac{1}{3}})^2=6V^{\frac{2}{3}}$
We restrict $V>0$.
