The problem I'm having is my 74HC595 is only outputting high on all output pins. The code is http://www.atomicvpp.com/LED_Cube_Final.pde. I have the wiring correct so I believe this is an issue with the software. ( I have an IC tester available and the chips are good) Any help would be appreciated. I can get pictures if you need.
Do you have OE/ connected to Gnd, and MCLR connected to +5V?
A 3x3x3 cube is small enough to run without shift registers, you could bypass the shift registers, wire it to your arduino, and test it (using a similar program).
I did it to a similar program for a 4x4x4 cube. I started with a program that runs the cube lighting one LED at a time, then modified it to use 2 shift registers, which changes it to lighting up to 16 LEDs at a time.
I have a 4x4x4 cube program that uses 2 shift registers (16 bits), If you want it, I can post a copy of it for you.