Can we do that?
Yes, there are certain rules though. Like you can't be at war and you can't change capitals continent unless the current one is surrounded.
Sometimes changing is important in terms of advantages if you are certain nations. Like if you can move it to an "inhospitable" province you lose that penalty on attrition and colonization.
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Iirc, this feature was added in NA (though, I bought Complete, so i'm not sure). You change it by clicking on the province you want to move it to, and clicking on the Crown in the top-left. The province must be core, and on the same continent as the existing capital. Or, the capital is landlocked and surrounded or is an island, then it can be moved overseas. It costs 1000 gold, and also carries a fair stab hit (I can't remember, it's either 3,4 or 5).
If you're playing vanilla though, I believe the only way is editting the save.
Give a man a fire, and he'll be warm for the rest of the day.
Set a man on fire, and he'll be warm for the rest of his life.