I finally was able to find help on this problem and mine now works.   I will try to tell all of  you how they fixed it on my phone.

1.  Go to Settings; Mail, contact, Calendars;
2.  Delete the accounts for calendars (not your icloud)
3.  add account, type Exchange  (here I am a bit forgetful on the exact set up, but found it online when researching this problem).  It is a multi-step process, so do find those instructions.
4.  Fetch should say Push

Now the Google part (this is where the online help I found stopped and why it did not work)
1.  sign onto Google
2.  go to settings (where the little gear thing is on the upper right of screen)
3.  Mobile Setup
4.  Mine is now done so I can't see what it said before but you have to enter your phone number, get a verification code, enter the code....   basically follow the bouncing ball.  

After that it all works, BOTH DIRECTIONS!!!

Why it is easy for some (my daughter's IPhone and granddaughter's IPad both worked right away) and for others it is a nightmare, I cannot explain.    But at any rate, this should do it.

Best of luck.