===== Answer =====

There will be 44 cubes with black paint on two or more surfaces.

Only the edges have paint on 2 or more surfaces. There are 12 edges which each have 5 cubes. If you take 12*5, you will count each corner 3 times, so subtract the repeats.

#edges * #CubesPerEdge - 2* #corners = 12*5 - 2*8 = 60-16 = 44