Calendar for websitewith google

I currently use google calendar for my website. The calendar gets updated automatically when someone books an appointment and displays as "busy". I was wondering if it is possible to have a calendar on my website which gets its info from my google calendar but for times not booked it will display "available" and then when someone does book it is replaced with the info received from the Google calendar. I don't know if it is possible. Example: Monday times are 7am and 8am. 7am shows available but 8am shows busy. Someone books 7am and that info is updated on the google calendar and then updated on the website calendar making 7am change to that info it got from google.