If you have a website that contains a calendar, the best way to make it public is to have an automatic export. That way you don't have to do any double work mwhile editing, as your events will automaticall be publicly available.
To do this seems to be around 4 hours of work for a web developer. Most programming languages has libaries for exporting .ics/iCalendar files. If you happen to ise WordPress together with the plugin "The Event Calendar", then .ics export is already baked in.