There are 2 ways I know of.
The first way, which I haven't tested out because I've never used the site, is Zapier. There are various actions you can choose on this page which seem to include posting events as they are created. I don't know how the post will look, if it works with recurring events, or if it works with user accounts or Like pages only, but it seems likely to be a good fit. There are also choices to post an event shortly before the event if you want to use multiple actions.
The second option is with your calendar's rss feed. You can get the xml link to your Gcal in the individual calendar's settings(hover over the calendar's name in the sidebar, click the arrow that shows up, and choose "Calendar settings") and use an rss-to-Facebook service like RSS Graffiti, IFTTT, Zapier or Networked Blogs(I am not affiliated with any of these) to post new items to your Facebook page. Google Calendar organizes the rss feed by date created, rather than by the event date. The benefit is that things are posted to FB within an hour(depending on rss-to-FB service) of making the Gcal event. The drawback is that recurring events are only posted when they are created, but not when they happen again. Also the details will be formatted like this:
Who: [your name, and this line only shows on events shared with you]
Where: [this line only shows if a location was specified]
Event Status: confirmed
An rss-to-FB service might have the option of leaving out the details, but the event date is only in the description. The event status is odd to include in a FB post and will get repetitive being on every post, so this may not be optimal.