Q: how can I sync my icloud calendar with a google calendar

The calendars reside on different servers and as far as I know there isn't a way to sync between them.  You can, of course, add your Google calendar to your devices and continue to use Google to keep it in sync.  If you open the Calendars app on your devices and tap Calendars on the top left, then tap Show All Calendars, your Google and iCloud calendar events will appear together your calendar.  You will only need to decide which one you wish to use as your default when adding new enteries, then set this in Settings>Mail,Contacts,Calendars>Default Calendar.