Differential expansion. Run the hot water until it gets really hot, then hold the cap end of the lens in the water for about two minutes. The cap will come off. Of course the lens will be destroyed, but at least you'll have the cap off.
Water is obviously not a good idea. Try putting the lens in your freezer for 5 minutes. The metal mount will contract faster than the plastic lens cap allowing the cap to be removed. Another method would be to get a small strap wrench. You should be able losen the cap with the wrench, if not consider the freezer method plus the wrench. I have used the freezer method to succesfully remove an overtightened filter.
Forgive me if this is a dumb suggestion, but are you sure you're trying to turn the lens cap in the right direction? The caps bayonets on rather than screws, and I've never known of a Nikkor lens where the cap was really stuck.
With the lens held so that the body mount end is facing you, the cap must be rotated clockwise to remove it. This is the oipposite direction to some other camera brands.
By the way - please don't try the "hot water" idea - I'm sure this was put forward in jest
The clockwise/anti clock thing really does happen. I purchased a 24-120mm VR f/4 Nikkor recently and tried to get the back cap off to mount it on my D700. No amount of my super strength short of harming the lens, the cap or myself could remove that cap. Fortunately, I'd purchased the lens locally and was able to return to the store and ask that the problem be resolved or another new lens substituted.
There was a bit of embarrassment when my sales guy simply turned the cap clockwise and, of course, it slipped easily off. I own and use a half dozen or so Nikkors and have owned and used Nikons since the very early 1960s (making me a genuine old-timer) beginning with a gem of a Nikon S3.
I suspect that when all clocks turn digital (as they nearly have), the whole concept of clockwise will become meaningless.
on my recent D3200 Kit lens (18-55) It didn't even have the familiar Black Plastic cap on the back end of the lens, instead it had a cheapo thin plastic milky white looking cap that (resembles the plastic of a Milk bottle) and it press fit. So you don't even twist on you just wiggle it on or off (press fit) I don't know where you would even buy the familiar twist on caps
Heat causes metal to expand. Being a metal mount it will expand faster than the cap. Conversely, cold causes things to contract or get smaller. The metal mount will contract faster than the cap when exposed to cold.
You'd be safer returning it for an exchange or refund rather than doing something that might damage the lens. The cap is plastic and if it's on that tight, something is wrong. Maybe a person at the factory was having a very bad day when this lens was packaged.