I ordered the Rainbowduino from Amazon too, via MKC Electronics, and received v3.0b, which I believe to be the most recent version.
An RGB LED is really 3 LEDs in one package sharing a common anode or a common cathode. The Rainbowduino supports 64 RGB LEDs. If instead you want to support single-color LEDs, the board should support 3 x 64 = 192 of them. A 5x5x5 cube is 125 LEDs, so that is feasible. Another approach can be found for an 8x8x8 cube, and boards are available for that as well from someone in Holland, but that would not be supported by Rainbowduino directly.
The Rainbowcube kit schematic (http://seeedstudio.com/wiki/images/d/dc/Rainbow_Cube_Kit_-_RGB_4x4x4_LED_schematic_board.pdf) uses only a few parts beyond the LEDs and should give you hints for the hardware arrangement you need.