Why you have that hum
Short answer: Electricity will find the shortest route to ground itself. It WANTS to ground itself, even if that means going through your expensive amp, or through your XLRs. In the US, electricity “pulses” sixty times a second (60hz), which produces a very distinctive hum; a sixty-cycle hum.
You can eliminate the hum by making sure everything is grounded, or at least everything is on the same power circuit, so that it grounds to the same place. Also, some musical equipment has a “ground lift” switch which eliminates the hum.
One more thing, if you put lighting equipment on the same circuit as the sound system, you WILL hear any lighting changes you make. It’s always smart to separate the two.