LED cube on arduino

Can any one tell me how to do this with arduino and not the atmel chip itself. Its a 8x8x8 one and there are so many wires for different layers. Can my uno handle them all? http://www.instructables.com/id/Led-Cube-8x8x8/

The latches or shift registers take care of the 64 outputs and use 3, 9, or 12 pins. I recommend using 8 shift registers connected to the SPI pins (SS->latch, SCK->clock, MOSI->data). Then you can use the SPI hardware to output 8 million bits per second. You can even add a 9th shift register to drive the layers and have the whole thing take only three Arduino pins.

You could also check out the part of the instructable where is tells you how to use an Arduino to drive it.