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