RGB SMT LED Cube, resistors, drivers, and shift registers.

I think i have a couple 3.3k, but not 3. and I dont think i have anything close to 1.8k.

I just made up this little schematic to show one layer of the cube.

It shows the cathodes connected (this is physically how they are connected too)

The anodes are connected to the next layers anodes, but im only showing one layer in the schematic, or it would be very hard to read.

16 RGB LEDs means 48 Anode pins to control, but only one cathode.

I do like idea of each layer having common R anode, common G anode, and common Blue anode, then it would be 16 cathodes and 12 anodes. I just dont see a way to do that, and make the cube dimensionally stable. The way the cube is built now is pretty dimensionally stable