My "Hummer" is driving me nuts

I am new to tube equipment, so know very little about it. I purchased a British-made Grant power amplifier, 50 watts? per channel, four large tubes, four small ones. Sounds terrific, however, when the volume is turned all the way down, I can hear a low-frequency hum from both speakers. Not loud, but definitely discernable. Increasing volume does not affect the hum. I have ruled out the preamp as cause, having swapped in a second pre, also ruled out cable interference, as I've set up the system in two different rooms with different configurations and different cable and hum remains constant. My questions are, what might be the source of the hum? Will swapping out tubes eliminate it? Any suggestions on what steps to take next? Thanks! Ben