If you have a public Google calendar, you can share it with visitors to your website. Any updates to your Google calendar are automatically passed to your website. (You cannot change the calendar from your website; you'll have to do that within your Google account.)
There are two parts to connecting the calendar to your website. This article explains the first part, which is how to copy the iCal URL from your Google account. The article for the second part explains how to Display a calendar on my website.
Note: Be sure the calendar you select includes future events, or Website Builder will tell you that it couldn't find any events in the calendar.
Note: Be sure you copy the iCal link. GoCentral only recognizes iCal as a valid Google calendar to import.