Enable Gmail Push for an Existing Google Calendar Account in iPhone
To enable mail synchronization for a Google Calendar account you've added to iPhone Calendar:
Tap Settings on the iPhone Home screen.
Select Mail, Contacts, Calendars.
Tap the Google Calendar account under Accounts.
Make sure ON is selected for Mail.
Press the Home button.
To enable mail synchronization for a Google Calendar account you've added to iPhone Calendar:
Tap Settings on the iPhone Home screen.
Select Mail, Contacts, Calendars.
Tap the Google Calendar account under Accounts.
Make sure ON is selected for Mail.
Press the Home button.