- You're missing
www in your regex
- The second
\. should optional if you want to match both youtu.be and youtube (but I didn't change this since just youtube isn't actually a valid domain - see note below)
+ in your regex allows for one or more of (youtube\.com|youtu\.be), not one or more wild-cards.
You need to use a . to indicate a wild-card, and + to indicate you want one or more of them.
Try:
^(https?\:\/\/)?(www\.youtube\.com|youtu\.be)\/.+$
Live demo.
If you want it to match URLs with or without the www., just make it optional:
^(https?\:\/\/)?((www\.)?youtube\.com|youtu\.be)\/.+$
Live demo.
Invalid alternatives:
If you want www.youtu.be/... to also match (at the time of writing, this doesn't appear to be a valid URL format), put the optional www. outside the brackets:
^(https?\:\/\/)?(www\.)?(youtube\.com|youtu\.be)\/.+$
youtube/cCnrX1w5luM (with or without http://) isn't a valid URL, but the question explicitly mentions that the regex should support that. To include this, replace youtu\.be with youtu\.?be in any regex above. Live demo.