Cannot sync iphone contacts to Googlemail

Hi everyone,

Im trying to figure out if I can transfer or backup the contacts I have on my iphone to my Gmail without plugging the phone into a computer etc.

I have an Exchange account set up, and icloud syncing contacts etc... but the new contacts I create on the phone DON'T seem to transfer over to my Google account contacts list...

Is this something Google no longer supports? I was sure that it would work but it doesn't...

I don't often plug my phone in and I create a lot of new contacts regularly on the go, and want them to be stored in Gmail automatically...

Please help!!!

WHat am I doing wrong??