A cube has numerically equal volume and surface area. The volume of such a cube is:

If $\alpha$ is the side of a cube, its volume is ${\alpha }^3$ and area of its six faces is  $6{\alpha }^2$ . Since the numerical values of volume and surface area of the cube are equal,

${\alpha }^3=6{\alpha }^2\Rightarrow a=6$,  

Volume of the cube, 

$V={\alpha }^3={\left(6\right)}^3=216units$