My calendars got synced in my phone. My custom calendar gets synced with Google in both directions. If you need it to be done on the server's side, probably you might try this:
I won't say it will work the way you ask, but at least they announce the following as key features:
1. Integration to other calendars: Publish your Roundcube calendar to Google Calendar and Apple iCal to view all your schedules in one place.
2. Integration from other calendars: Link and view all scheduled events from Google Calendar and Apple iCal in your Roundcube Webmail calendar page.