You can make all of your Zimbra calendars viewable from your Google Calendar account. To do this:
1. Log in to your Zimbra account. Navigate to the calendars panel.
2. Find the calendar you would like to share.
3. To the right of the calendar, select the hidden icon. There, you'll find an option to share your calendar.
4. When you select share calendar, this window should pop up.
5. Select 'Public.'
6. Copy the link marked "ICS."
7. Navigate to your google Calendar. Select the arrow next to 'Other calendars.'
8. Select "Add by URL" in the arrow next to "Other calendars."
9. Paste the ICS link.
10. Wait. Do not close your window.
11. All your events will now be visible in Google Calendar.