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

Hippynerd:
I think i understand the basics of the calculations, but it would be nice to understand why the parts are needed.
Which parts? Are we discussing the common emitter circuit?

I also dont like the guessing part of the calculation, it seems to me that the part will likely behave about the same under similar conditions for most people.
It's not a "guess". You have to start somewhere. Having only the least is a good start, if there's more (as in more beta, as may be likely) then it only gets better. The circuit will not be a worse performer for the transistor's having more beta (gain) than anticipated.

It seems like it should be easy to look that up in a chart or graph, and get close with your calculations, but I wasnt able to do that, I had to test things, before I could get in the ballpark.
How can I know where you're losing the plot? You haven't shown your work.

I can't see what's going on in your schematics; they're pretty free-form, difficult to follow.