I am using a google account. And I want to sync the SharePoint calendar events with my google account.
How to sync SharePoint calendar or list with google calendar?
Google has a .NET api that you can add to your SharePoint project.
You can then use it to access the Google Calendar directly without using web services, and update the events to be in sync with the SharePoint calendar.
There's a nice walkthrough on how to use the API here: http://www.codeproject.com/Articles/196548/Managing-Google-Calendar-Events-using-NET
There are some similar articles for your reference.
Sync calendar between SharePoint, Google, Outlook http://kmlsp.wordpress.com/2012/02/06/sync-calendar-between-sharepoint-google-outlook/
Sync Google Calendar with SharePoint Calendar http://www.rssbus.com/kb/articles/ado-google-sp-calendarsync.rst
Keep Your SharePoint Calendar Synced with Google http://geekswithblogs.net/Lance/archive/2010/01/13/10-diy-sharepoint-web-parts-10.aspx