I used common anode (positive) for each floor and common cathode (negative) for the 9 columns.
The animation (the 1st two of them) uses Multiplexing, the rest of the animations just runs thru the floors one at a time.
I control the cube with 4 Shift Registers (No needed really for a 3x3x3 cube as Arduino can easily handle it) but the idea is to learn how to use them, just in case I make the jump to a 5x5x5 cube hopefully RGB.
I'm going to add more info in a blog I'm making, you can get some extra info, plus a PDF as a "Guide" to make one of this.
http://arduino.alt245.com.ar/3x3x3-led-cube/
It's not perfect, but it works, I have a lot more to learn and to improve. But it's a starting point.