Your Subject says one thing, and the body of the post says another.
Where is this calendar and what do you want to do with it?
Your Subject says "How can I sync a calendar "ON" SharePoint 2013 online, to a 365 Calendar?
That is telling me that your Calendar is already in SharePoint Online, and you want to sync it to your Office 365 Mailbox calendar.
The body of the post says "Is there any way to sync a calendar that is in Outlook (Exchange 365 Mailbox), up to SharePoint Online.
So,im not sure what your asking but let me give you your options.
This is very easy, but you have to pay attention to the Flow of things.
- The Calendar Must exist in SharePoint First. So, If your Calendar is already in Outlook, you need to log into SharePoint and create your calendar where ever you want it to go. Then you will click the "Calendar" tab on top left, and then click "Sync to Outlook". This will sync the blank calendar to your outlook.
Next, you need to go to your main calendar you want to sync, and change the View to "All Items", you then want to copy all items and go to your new calendar change view to All Items, and paste in your items. This will get all the items synced up to SharePoint.
Now you just need to tell everyone to go into SharePoint and sync that calendar down to outlook. Now just make sure everyone uses that calendar.
So, whatever you do, the calendar needs to start in SharePoint.
Hope this helps