The hum exists as follows:

With the sub plugged in and powered on but no LFE connected it hums and the hum gains in volume when you turn the volume gain up on the sub.

With the sub plugged in and powered on AND the LFE connected it hums louder in volume, relative to without the LFE connected, and also increases in volume as you turn up the volume knob.

If you touch the tip of your finger to the speaker posts on the back of the amp with sub powered and either the LFE connected or disconnected you also hear a humming noise.

If it is truly a ground fault issue is there any device that can be purchased and placed in line to eliminate it? I have plugged the sub into multiple circuits even circuits that run through two different panel boards and have also plugged it into outlets that are the only outlets on a single circuit such as sump pump outlet or my outlet on the wall that is directly wired to the panel board and the noise is still there so I have eliminated the possibility of any other devices on the circuit causing the hum.