Hi! I have a subpanel in the detached garage that is fed by a 6/3 sheathed electrical cable, protected by a 50-amp double pole circuit breaker. On this, I have about 4000 christmas tree light bulbs. I added-up the power of every bulb, and the total I calculated is 6110 watts. The lights run on 120 volts. Last year, I realized that when my system switches on the lights (spread out on 6 15-amp circuits), the lights in the garage slightly dim, and after a couple of hours that the lights are on, the 6/3 sheathed electrical cable is slightly warmer to the touch. Does it mean that my circuit is overloaded? I would like to add some more lights; would I need to upgrade my system? The main breaker box is 200 amps.

Also, I know that the maximum watts capacity of a 15-amp circuit breaker is 1875 watts, and you should observe a safety tolerance of 20%, which means I should not plug more than 1500 watts on that circuit. Is this rule true for light bulbs? I know it does not apply to motors because they are "inductive loads". Please help! Thanks.