Yes, in a cube and a square which is a face of the same cube, the side length is the same. Use that side length, s, as the "connection". The volume is proportional to : . And the area is proportional to the area: . Eliminate s from those two equations to get a formula in only V and A.
(And what you give: does NOT say "volume is proportional to area", it says "volume cubed is proportional to area squared".)