The side of a surface is: \(\sqrt{\left(96:6\right)}\) = \(\sqrt{16}=4\left(cm\right)\)

So the volume of the cube is: \(4.4.4=64\left(cm^3\right)\)

:v oh..... i'm wrong !!! 

Area on one face is :

\(\dfrac{96}{6}=36\left(cm^2\right)\)

The length of an edge is :

\(\sqrt{36}=6\) (cm)

The volume of the cube is :

\(V=6.6.6=6^3=216\left(cm^3\right)\)