If you need make a room mailbox public, for example for a public event, these few PowerShell commands will help you:
First, connect to Exchange Online with your tenant admin:
Connect-ExchangeOnline
Make the calendar public and make the calendar entries visible to everyone:
Set-MailboxCalendarFolder publicRoomMailbox:\Calendar -PublishEnabled $true
Set-MailboxCalendarFolder publicRoomMailbox:\Calendar -Detaillevel Full
Show the HTML and iCalendar URL:
Get-MailboxCalendarFolder publicRoomMailbox:\Calendar | fl published*
The URLs can be shared with anyone or the HTML URL could be embedded on a website as part of an iFrame.