Need help with optimization problem

I need to solve:

A manufacturer wants to design a closed box having a square base and a volume of 125 in^3. What dimensions will produce a box with minimum surface area? V=x^2y, S=2x^2+4xy

The problem is: Maximize 2x^2+4xy subject to (x^2)y = 125 and x, y are positive.
Solution substitute y = 125/x^2 to get max. 2x^2+ 500/x. Differentiate: 4x - 500/x^2 = 0 , x^3 = 125,
x = 5 , y = 5. So, the answer is a 5x5x5 cube !