It's not quite a cube... :
The Arduino is connected to 4 Allegro A6276EA LED drivers for the control. Cube is built in common anode configuration from 512 3mm high brightness leds. I'm using a computer power supply to provide 5 volts to the cube and the Arduino.
Took about 2 weeks to build. It should have been less but I had other projects going on. Last month I built a 4x4x4 cube using 1 A6276EA chip as practice. That one worked fine so I ordered 1000 LEDs off eBay and scaled the code up to 8x8x8.
Hope you like,