how much does it cost to repair the iphone 6 home button?

https://www.apple.com/support/iphone/repair/other/

Price can be different depending on location/country, you can use google if you don't live in the U.S.

Apple will not replace your home button, they will only replace the entire device for an out of warranty fee. If your screen were cracked and you paid for a screen replacement, they would install a new screen with new home button. One thing to keep in mind in the mean time is DO NOT UPDATE IOS if your home button or touch ID are not working. This will result in the infamous "error 53" which will completely brick your phone. Your best bet would be to try and get a screen replacement at Apple even without a damaged screen. I don't know if they will do it, but that is your only real option for i6 home button repair.