The 4x4x4 cube and the 4x4 square use the same code base. There is every little difference between the code used between the two devices. As of 09/04/2012 the only difference is the LED used to show "demo" mode. I expect some changes in the pattern tables in the near future that would be difference between the two products.
Near the top there is a "#define" to enable the code for the 4x4 cube.
I used Simon Inns "Building_a_PIC18F_USB_device" as my starting point.
If you can't get it to build, have some questions on the code, or created something cool that you want to share just send me email at email@example.com.