8x8x8 LED Cube

I'm working on a project to build an 8x8x8 cube. I want to use a total of 9 shift registers (74HC595) to control the cube, 8 for the 64 columns, 1 for the 8 levels.

I don't understand how to write the code properly to light it using the shift registers.

The video of that 8^3 cube is awesome!