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. Apparen

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