Updating Xcode looping the download process
I had issues to download Xcode 8 from App Store too. Just when is going to finish installation process, something happened and Xcode started downloading again.

I just needed Xcode 8 installed as fast possible. So I just passed to another step.

Thank you Apple, for dev apps there is a alternative to download them. Any version of Xcode and its tools, you can download through developer.apple.com, to check all tools that you can download come to this link. If you just need Xcode 8 this link is your friend.

Now I have Xcode 7 and 8 in my system. You can delete your old Xcode 7 if you want.

Sure, you need at least a free apple dev account to download them. Just enter your appleID and agree to Apple terms.

Note: App Store shows me to update Xcode, maybe because I still have Xcode 7 installed.