Here is a way to build a 2^6 cube

[Manfred K. Warmuth]

It generalized to 2^12, 2^18, ... , 2^(6n)

You can build a prototype of a 2^6 using 4 of Melinda's 2^4.

But is a better way to do it by thickening the color caps of the cubies.

More about this later.

Enjoy

https://www.youtube.com/watch?v=yALpt6W3QWI