I read somewhere that udo krell said that he "pulled out the corners and edges of the 3x3, and shoved the other pieces in between" to make the 5x5x5. Why couldnt you do that to a 5x5x5 to make it a 7x7x7?

I have a design for a 6x6x6 that seems possible, but i cant build it. it involves a spherical inside, and 2 circles on each "face" layed out on the sphere.
Its pretty much taking a 4x4, and doing what udo krell said... except instead of shoving the other pieces inside to hang on to the other pieces, it would have connectors inside the sphere like the 4x4 centers

When the top face of a 7x7x7 cube is turned, the corners would stick off the edges so far that they had nothing to hold onto. So either the cubies need to be different sizes, or something else clever...

i know about that, and today, i proved it physically. When i complete the 7x7 extend with stickers, ill show a pic demonstrating the "corner hangover"