These instructions for setting up an Office 365 Resource Calendar Externally are assuming that you have already created the calendar in Office 365

Step 1

Log in to the Office 365 Tennant via Powershell

How to Connect to Office 365 Exchange Online using Remote Powershell when MFA Enabled5 (1)

Step 2

Run the following command

Set-MailboxCalendarFolder boardroom:\Calendar -PublishEnabled $true

Where boardroom is the name of the Mailbox that holds the calendar

Step 3

Run the following command

Get-MailboxCalendarFolder boardroom:\Calendar

Copy the external ics or html url from the results

Step 4

Run the following command

Get-Mailbox "Boardroom" | Set-CalendarProcessing -ProcessExternalMeetingMessages $true

Where Boardoom is the identity of the Calendar

Now that you have the published ICal URL this can be added to Outlook