A solid $6$-by-$6$-by-$6$ cube is constructed from unit cubes and the entire outer surface is painted. What fraction of the unit cubes has at least two painted faces? Express your answer as a common fraction.
8 cubes will have paint on 3 faces
4 * 4 * 3 = 48 will have paint on two faces
[ 8 + 48 ] / 6^3 =
56 / 216 =
7 / 27
