Would building one be cheaper than buying one? I'd imagine the most expensive components to be the speakers themselves; but with a little patience and logic I don't see how it couldn't be too much money or time.
Depends. Do you have tools? If you have a table saw or Circular saw, a jig saw or router for the speaker holes, and a drill with small bits, and probably some clamps and wood glue.

Not a huge list but it can be if you dont have anything.
building should be cheaper than buying. never built a cab so i dunno but if it's like anything else it should be cheaper to build than buy.