Discussion

Explanation:

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Let us first consider middle of the edges:
The top 4 edges, will give 3 such cubes each, hence total 12 such cubes.

Out of bottom 4 edges, only 2 edges will give 3 such cubes each, hence 6 such cubes.

Out of vertical 4 edges, only 2 edges will give 3 such cubes each, hence 6 such cubes.

Now, corners:
Out of 8 corners, 5 corners will have exactly 2 colors on them.

∴ Total number of cubes with exactly 2 colors on them = 12 + 6 + 6 + 5 = 29.

Hence, 29.

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