To sync your Google Calendar data between Google cloud and Android, you need the Google Calendar app. Alternatively you can configure Google as Caldav calendar, but this has several limitations.

Early versions of Android included a Google Calendar sync adapter, but this was moved to the Google Calendar app, to be able to update via Google Play.

The Google Calendar sync to Android has some limitations:

Past events limited to 12 months*

Future events limited to 12 months*

Google calendar offers 11 event colors.

Attachment sync is not natively supported by Android, but can be activated per calendar in the calendar list.

*You can view all your data online in Google Calendar in a web browser. To sync all past data to Android, see (Past / Future) Entries are missing