Hi Ricardo,
Thanks for stopping by! At the moment, I’m afraid that we don’t offer any automatic syncing functionality for full calendars created with The Events Calendar or Events Calendar PRO. Users may export events (either individually or as a group) to import into the third-party application of their choice, but these exports are static files, and events that are exported and brought into another application will not change if the original event is updated.
We do have an existing feature request on UserVoice for something very similar that may meet your needs, if you’d like to cast your vote for this suggestion:
https://tribe.uservoice.com/forums/195723-feature-ideas/suggestions/6430110-subscribe-to-calendar-with-google-calendar
For now, I’d suggest that the best way for users to keep up to date with events that are posted to your site would be to subscribe to your calendar’s RSS feed. You can learn more about RSS feeds for calendar events on our Knowledgebase here.
I hope that helps! Thanks again, and let me know if you should have any other questions! 🙂