I did something similar with LEDs [not a cube, just a board with lights] to alert on various things before just having the Pi power an old wall mounted LCD I wasn't using anymore + a dashboard.
It is one of those ideas that is awesome in theory but its really hard to justify the time/effort beyond "FUN!"
The cube animation are six square divs animated with css. Just take a look at the source if you're curious.
Thank you for the advice about the cube, I will definitely have a look!