Can you put a V6 engine in a 4 cylinder 2003 honda civic?

How much would that cost?

A V6 Honda engine would almost certainly not fit in a Civic, there's no way to estimate any such custom work since my its nature is custom work.

Not without spending boat loads of money. Forget it.

Has been done, but unless you have some leet mechanical skillz yourself, it's going to cost more than just buying a faster car. (If you have to pay a shop to do it)

It's not a straight "drop in" and there's also the issues with cooling. Suspension, brakes etc as well, if you want the thing to actually drive reasonably. Getting the car certified as street legal will also be an issue in most places.

Anything can be done with money, Different engine, different transmission, different motor mounts and of course the computer, wiring and related items. My guess, 10k

Try a V8, its been done. Look it up.
Only those who done it can tell you how much it cost them.