This is helpful: Google Calendar .NET API documentation.
// Create a CalenderService and authenticate
CalendarService myService = new CalendarService("exampleCo-exampleApp-1");
myService.setUserCredentials("[email protected]", "mypassword");
// Create the query object:
EventQuery query = new EventQuery();
query.Uri = new Uri("https://www.google.com/calendar/feeds/[calendar]/private/full");
where [calendar] = "[email protected]" for default calendar or in your instance, the ID of your 'events' calendar (found in calendar in Gmail), that is, https://www.google.com/calendar/[calendarID]/private/full"
// Tell the service to query:
EventFeed calFeed = myService .Query(query);
// This should delete all items in your calendar
foreach(var item in calFeed.Entries) {
entry.Delete();
}