if i recall correctly, Engl taylors their power sections such that you can play them quietly, and still have good tone.
and, it kinda depends on your neighbors. i've had some pretty rock'n neighbors in the past. my neighbors in Cincy never minded when i'd crank my 2x12 Nomad, and my neighbor from last year actually requested it from time to time
if they're the quiet types, you may want to just get some nice headphones for your Cube. or, from the headphone jack, hook your amp up into a moderately sized stereo system.