This feature is available on Power accounts and higher.
Would you like to add a calendar to your SmugMug site so visitors can check your availability or find details for an event? You can do that with the Google Calendar content block.
In the navigation bar, select Site, then browse to the page you want to add the calendar, and click Customize Design in the section bar. Once in the customizer, on the content tab under Services, drag the Google Calendar content block onto the page.
Click the wrench icon on the content block to edit the settings.
In your Google account, go to your Google Calendar to locate the Google Calendar ID.
Note: The calendar needs to be set as "Public" on Google in order for this to work.
In the calendar list on the left, click the three-dot expansion menu next to the appropriate calendar, then select Settings and sharing.
In the Integrate calendar section, locate the Calendar ID. Copy the ID and paste it into the Calendar ID field in the content block settings on your SmugMug site.
See this Google help article for reference.