It is possible that there is a problem in the audio portion of the motherboard. The kind of phenomenum you describe occurs quite often in certain kinds of electronic circuits. The basic cause may be a faulty capacitor that does not discharge quickly enough.
This happens often with routers and modems where your internet connection fails to work and you cannot get mail or internet pages. The solution in this case is to turn off all power to your internet "system" including router, modem, Airport, etc. Then wait 30 t0 60 seconds and turn everything back on. Now, the internet connection is working.
While annoying, you probably do not want to have your system checked out by Apple Repair. This could cause more trouble then it is worth as they would probably replace the motherboard!! By the way, does the cube have an internal speaker? If so try using it.
MamaMoose