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

Look at the pin numbers on the bottom right diagram (you can ignore the zener diodes). The have drawn the image as if it were from looking at the back.
If you then look at the top left diagram, the cathode is marked with a triangular notch.

The good news is that if you have in fact wired everything as common anode, it is a lot easier to control as you can now use the TLC5940's or any other LED current sink to drive them.