CiviCRM Event can be integrated with Google Calendar.
- Have your Admin SDK and Google Calendar api enabled in https://console.developers.google.com
- Create Google app and have your client ID and client secret
- If your CiviCRM is already connected to Google app, you have to delete the access token in setting table in order to connect to new Google App.
- Install the extension manually in CiviCRM. More details here about installing extensions in CiviCRM.
- Configure Google Auth details in Administer >> System Settings >> Googlecal Settings(civicrm/googlecal/settings?reset=1)