AMC 12 2005a Problem 10

A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$?

$\textbf{(A) } 3 \textbf{(B) } 4 \textbf{(C) } 5 \textbf{(D) } 6 \textbf{(E) } 7$