Turning on and tweaking the noise gate is a band-aide and it can help...The root of this problem is often the pickups themselves in combination with extremely high gain...although your suspicion of the cable is well placed...but it seems you might have already elimiated that...

To make it even more wierd for you, I have personally had a problem with particular pickup rings that would resonate under high gain...Even the pickup springs can do this...It has been very rare that I have found a guitar in stock form that was 100% ready for high gain use...You gotta tighten down and dampen everything thing...pickup potting is the #1 culprit in my experience.

If the potting is decayed, non-existent or just done improperly then this is exactly what happens. Uncontrollable squeal..Epiphone stock pups are notorious for this (at least they used to be)...It does not matter if the guitar is new...plenty of new guitars do this...