When you want to use an external google calendar (for which you got invited), it's unfortunately not enough to add the google account to your iPhone. When you add the account, you're able to choose to show all your own calendars in your calendar app. But you won't see the external ones in the list.
You have to manually mark it as a calendar to be synced. You can do this on this page.
I have no idea why google decided to put those settings on an extra page instead of putting it into the calendar settings, but that's the way you can make it visible on your iPhone.