At the very least you would be infringing the person's copyright. Youtube videos are not in the public domain. So there is a copyright on them until 70 years after the author's death (or whatever the youtube terms of service specify). Thus, yes, it's illegal.

Also, the author has in all likelihood either removed the video or closed the entire account because he or she does not want this particular video to remain available on the web. So reposting is questionable from a moral point of view, as well.

For both of these reasons, the forum rules forbid posting (links to) re-uploaded material (Forum rule 1.10). If you browse, you'll find plenty of links deleted by Marty for disobeying this rule.

SC