Google Calendar provides API to integrate third party clients to retrieve or manage the Calendar data. Most complicated part of the integration is understanding, choosing right pattern and implementing the Authentication.
To integrate Salesforce with Google Calendar to retrieve details without having to require user go through the OAuth authorization, you would have to use Service Account scenario. This scenario requires Salesforce create a JWT token using RSA-256 encryption. Fortunately Salesforce added support for RSA-256 bit encryption in Summer 14 release. So it is possible to connect to Google Calendar API and retrieve the free/body information for users.
One caveat with implementation is that, Google requires to use URL Safe Base64 encoding (similar to what Commons Codec has done). This mode requires to replace + with – and / with _. If you forget to do this, the signature that your code generates will not match what Google creates for verification and it would return “invalid_grant” error message.
Hope this helps.