Problem of the "Week"

[MATh...@gmail.com]

For February 9, 2007:

Some of the faces of a large wooden cube are painted. The cube is
then cut into small identical cubes. The number of these small cubes
with paint on at least one face is 75,525. How many small cubes do
not have any paint at all?

Please do not post your answer here. Rather, e-mail your solution and
how you arrived to it to MATh...@gmail.com by February 23, 10 AM.
So, I suppose that makes it the Problem of 2 Weeks, but Problem of the
Week sounds better.