It appears that your administrator is blocking HTTP (port 80) to youtube, but as you can see you can get to the site using HTTPS (443). The reason is most likely that they are not intercepting and decrypting the SSL traffic (which can be done, but be careful if they do because they would have the ability to decrypt traffic to any HTTPS site including financial web sites).
After you make the connection you are still not able to see the video. This is probably because something in the rule set is preventing that traffic from passing.
You should note that if your organization has an information security policy, you should adhere to it. Trying to circumvent the policies could get you terminated if stated in the company policies. I would look into that if I were you.
Plase note that I have already made request for exception for my PC because my workplace requires access to youtube because I find many useful tutorials regarding IT but I am still waiting for administrator which is very busy at the momment, to add me to exception list.
In meantime, while I wait I would like to have access to youtube but I don't know how? I tried with unblockanything (dot) com but to slow. Can you suggest me any similar solution?