If it's 60 Hz hum (assuming you live in North America) then it's a power supply issue. Anything else is most likely interference coming from a PC component or perhaps a wi-fi router that's close by.
Try to write down the conditions when you notice any noise coming from your headphones or speakers. Were you moving your mouse? Playing a game? Accessing something from the disk drive? Note the nature of the noise too - is it steady (hiss, white noise) or intermittent (bursts of static).
Try moving sources of interference away from your setup or turning them off entirely. This includes mobile phones, Bluetooth transmitters, and wi-fi access points.
Good luck!