Discussion

Explanation:

Center of Faces:
Each of the 6 faces will give 3 × 3 = 9 middle cubes with exactly one color on them. Hence, total 6 × 9 = 54 such cubes.

Middle of Edges:
Three red edges and one yellow edge will give 3 such cubes, hence total 12 such cubes.

Corners:
One red corner will give 1 such cube.

∴ Total number of cubes with exactly one color on them = 54 + 12 + 1 = 67

Hence, 67.

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