To be able to do that you need to be able to manage all of the users their google calender API keys (or all other external API keys of all possible calenders), to have access to the calenders, an Entity should hold all the required data.
Then every user should grant the Mendix app write rights in his calender (The mendix app can be represented with a system user, or a user/password in constants).
After all that is done, you need to create a Mapping that is understandable by the calender API. more info about that is found ihere:
I hope this helps you a bit on your way.