This is not really a hard question (although I got it
wrong several times before I got it right due to
nervousness).  However, there is the hard way to solve it
and the easy way to solve it.

Hard way:

Try to add up all the cubes on the surface.

So the top and bottom are each 10 x 10, which is 200.  Two
more sides are 8 x 10 (since you don't count the two edges
already accounted for), which gives you 160.  The last two
sides are 8 x 8 giving you 128.  

So the answer is 200 + 160 + 128 = 488

Easy way:

The number of cubes on the outside/surface is simply the
total number of cubes minus the number of cubes on the
inside.

Total cubes - inside cubes = outside cubes
    10^3   -      8^3     =
    1000   -      512     = 488


Zach