The Core :

The Core is far more realistic than you would think. There is actually a huge nuclear reaction at the core over the Earth, which is why it is so hot and melt down there. If it were to ever stop, nuking WOULD restart it.

It wasn't a layer, it was a giant geode.

Best part of the core is when the black guy died for the white ppl tbh

The Earth's core is massive, you would need to add a ludicrous amount of energy to reheat it I think. Physics isn't my forte though.

...

All I remember from the Core is a pigeon flies into a window and a black guy dying in a tunnel.

Sunshine is great until the last act, when it turns into some stupid slasher flick.

Technically he died in the tunnel but it was because it was compressed around him.

The inner core is a giant lump of metals (iron, platinum, nickel etc) that is under such intense pressure that it can be incredibly hot (5.6k C if I recall) and still be solid. (Most metals have their melting points raised as they are under more pressure)

It's just really, really hot and not actually a nuclear reaction.
A nuclear warhead would not do a thing to it.

The sun, on the other hand, is nuclear fusion, caused by hydrogen atoms smashing into each other, creating helium and also releasing lots of energy, the radiation that causes it to be so hot and transfer that heat through space (radiation travels better through space than any other form of heat/energy transfer).
Technically, the sun could actually extinguish itself if the atoms stopped smashing into each other, but that's such a laughably low chance that it's never accounted for. I'm talking 0.1x10^(-10^1000000^100000^1000000) and beyond. Probably the only thing you could ever truly call impossible.

If, however, it did die off, the use of a nuclear warhead would probably actually work, provided it was a fusion bomb and not a fission bomb. Fission might work, I guess, but fusion would guarantee it.
Then again, you would only need to move a single atom of hydrogen for it to start cascading again.

The real trouble with the sun is that:
a) you can't get many things near it as it's so hot and dense (even after it stops fusing atoms), so you need an explosion to send a ripple of energy out to move the atoms
b) by the time it stopped working, we'd be dead before we could scrounge together nukes and ships

Thinking about it, The Core and Sunshine have swapped their science around. The sun needs a nuclear detonation to get enough energy through the heat and the inner core would need extreme heat from "dark matter" to get everything back to the way it should be.

because nobody fucking knows about the other one?

I wonder too, fellow obese litmus test for cancer.

Wouldn't Earth be a star if that was the case?

Not necessarily, you can have a natural nuclear reactor encased in crust.

wut?