Faint hum....


I've been struggling to understand this issue for a while...my integrated amp has 2 RCA inputs, 1 XLR input, and a few digital inputs (Toslink, Coax, etc). When I turn the system on, i'm usually on either RCA1 (CD player) or RCA2 (phono stage connected), there is a low hum in the speakers. If I increase the volume, it gets louder. If I mute the amp, the hum goes away. It's noticeable, but it doesn't bother me when the music plays. What I find it somewhat strange is that it has the same volume if i switch between RCA1 RCA2, and XLR (I have nothing connected to this input!!!). But when I switch from one digital input to another (Coax, Toslink1, Toslink 2), there is no hum. Everything is dead quiet.
So what's going on? Is there anything I can do to eliminate this hum? I tried all sorts of interconnects, speaker cables, the hum remains when I switch from one analog input to another. It might have different intensities, but no cable got rid of it.
iasi
Post removed 
Yes, if it's only a question of which input is selected, even if no component is attached to that input, then it obviously sounds as if the problem is internal to the amp, especially as digital input is quiet.  Hum on any/all of the line-level analog signal inputs, then?  What make of amp?
yeap, a faint hum on any of the analog inputs...it doesn't go up with the volume...but it's there...Gold Note IS1000. Not planning to replace the amp since it is the most musical one i've had in my system...
If the hum is coming from the speakers and not from the unit itself, then it is likely a ground loop.