**Solution**

Let each side of the cube be $a \mathrm{~cm}$.

Then, the total surface area of the cube $=\left(6 a^{2}\right) \mathrm{cm}^{2}$.

$\therefore \quad 6 a^{2}=216 \Rightarrow a^{2}=36 \Rightarrow a=\sqrt{36}=6$.

Volume of the cube $=a^{3} \mathrm{~cm}^{3}$

= (6×6×6) cm^{3} = **216 cm³.**