Vanilla extract cups vs spoon
I don't think you can salvage that cake. That's just way too much vanilla, and you can't take it out.

You could take out enough to have two (tea?)spoons of vanilla, though, and use that in a new cake. For example, if the total volume is now 6 cups, and 2 cups of it is vanilla, you'd need 6 teaspoons of it to get 2 teaspoons of vanilla. You could then make the cake over again, and use that instead of the vanilla you'd have added. (Yeah, you'll get a little extra of the rest, but it's a small amount, it should be fine.)

To try to save the rest... all I can think of is freezing it to try to preserve it, so you can use portions of it to replace vanilla similarly in future cakes. With that much vanilla, I don't know if it'll actually freeze solid - it's mostly alcohol. So I might try putting it in an ice cube tray, in case it does freeze solid (so you put the cubes in a bag and still get individual portions) and then if it stays soft, you can always put it in a single container to scoop out of. Vanilla is pretty volatile, though, so use an airtight bag/container and don't expect it to last forever.

If it's vanilla syrup, the same generally applies: you have way too much, and you can't separate it. If you go the freezing route to try to save it, syrup also doesn't freeze very solid, thanks to the sugar, so same potential issue there.