I was about to ask this question "Which package managers can transfer packages via BitTorrent?" on Unix & Linux SE but I hesitated in posting it. See I thought that maybe it would be considered to have too many answers for it to be acceptable to this site.
If you want to ask anyway, you need to keep the question as narrow as possible, so it's actually answerable:
- Limit it to Linux distributions at least. The more you limit it, the more answerable it becomes.
- Explain why you want to download packages over BitTorrent. Practical problems tend to get better answers (including, possibly, some different solutions that you never thought of) than "sounds like it'd be cool".
- Be aware of existing related stuff, and mention it as appropriate. E.g., you can get CD/DVD/Blu-Ray/etc. images for most distros via BitTorrent. Or (for the case when you want to save bandwidth updating your dozens of machines), many package managers have caching solutions so you only download the package once, then the cache serves it to the other n machines.
You could also consider asking on Software Recommendations, if you can make your question fit their rules.