Is this a Suburban water heater? If so, the drain plug is also the anode rod. And it should be replaced when depleted, typically every couple years, or sooner if using a magnesium rod.
I would use a 6 point 1 1/16" socket with a long breaker bar to try to get it out. The 6 point socket will reduce likelihood of rounding out the hex head. Apply force in the loosening direction, then apply force in the tightening direction. Keep repeating until it finally gives way. Brute force, whether with the breaker bar or impact, should be the last option.
And when you put it or a new one back in, do not over tighten it. Those are pipe threads and do not need to be screwed down very tight to seal.