I just saw a website offering this service "cpanel3" to their customers. Is this software I can purchase/license independently or is this something I can only use if I am hosted with a particular upstream provider?

Here's the link to the software:
http://www.100megswebhosting.com:2082/frontend/default/index.html

Use the following login information -
Username: testing5
Password: testing5

Visit http://www.cpanel.net and you will find a link to all distributors of CPanel. But be warned, it's not cheap.

I read over at http://www.burst.net/cp/ that it's $99.95/month/server for external licensing. Does this apply to each domain that's hosted on my server or is just just per physical server that cpanel sits on?

Suppose I have 50 websites hosted on one machine. Is it still $99.95 per month?

I'm guessing, but I'm not sure, that it is per physical server. Otherwise hosting would cost A LOT more then it does now!!

NO, it's per server and not per domain. This means that you can host unlimited amount of domain on one server. If you go to another server you must purchase another license.