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No. There are 3 faces, to start with. Also there are two circular edges. But you are correct in the number of vertices.
With ms paint, use the pencil tool and cut and paste the picture
Answer = 8. The only small cubes with paint on three faces are those that occupied the corners of the original cube.
Total number of faces = 9*6 = 54 Number of "hidden" faces = 2*(9 - 1) = 16 So number of painted faces = 54 - 16 = 38
There will be 64 cubes total.The original 8 corners will have three red faces.The cubes that came from the original 12 edges excluding the original 4 corners will be 24 with two red faces (adjoining faces).There will also be leftover 24 cubes with one red face and 8 cubes with no red paint.8+24+24+8 = 64