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Hmm, it looks like even a 7x7x7 doesn't need to have much. I guess it has a tiny amount larger edge and corner pieces though...

https://www.amazon.com/Shengshou-7x7x7-Cube-Puzzl-black/dp/B...

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You are correct, the 7 x 7 x 7 is the minimum where a perfect cube of cubes is impossible. The Wikipedia article shows the issue with the corner cubes.

Apparently the 7-cube bulges slightly which helps to hide that the larger sized edges / corners

https://en.m.wikipedia.org/wiki/V-Cube_7

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