I think the answer is 18 because
a cube has 6 face and 3 cubes have 18 faces.
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There are 6*6 = 36 faces in all.
1 cube has 6 faces therefore 236 cubes have 1,416 faces.
This is kind of neat. I drew a three dimensional cube. Then divided the faces into 16 squares per face. Then started counting which of those little cubes would have a painted face. I get: 1 red face - 24 cubes 2 red faces - 24 cubes 3 red faces - 8 cubes 4, 5, & 6 red faces - 0 cubes
six faces
6