The volume of a cube is 729 cm

Let $a$ be the length of the edge of the cube.

Then volume $=a^{3}=729 \mathrm{~cm}^{3}$

Also, $a=\sqrt[3]{729}=9 \mathrm{~cm}$

$\therefore$ Surface area $=6 a^{2}=6 \times 9 \times 9=486 \mathrm{~cm}^{2}$