The volume of a cube is 512 cm3.

(b) $384 \mathrm{~cm}^{2}$

Suppose that a cm is the edge of the cube.
We have:

$a^{3}=512$

$\Rightarrow a=\sqrt[3]{512}=8 \mathrm{~cm}$

$\therefore$ Total surface area of cube $=6 a^{2} \mathrm{~cm}^{2}$

$=6 \times 8 \times 8 \mathrm{~cm}^{2}=384 \mathrm{~cm}^{2}$