2008 Pascal Problem 17

The surface area of a large cube is 5400 cm^2. This cube is cut into a number of identical smaller cubes. Each smaller cube has a volume of 216 cm^3. How many smaller cubes are there?

\textbf{(A)}\ 25\quad \textbf{(B)}\ 125\quad \textbf{(C)}\ 164\quad \textbf{(D)}\ 180\quad \textbf{(E)}\ 216

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.