Sci-Hub is a paywall-bypassing website that uses "shared" user credentials to provide PDF or HTML scientific papers. The website itself doesn't store any papers. (There are interesting comments on your same question on another site.)
But LibGen (via wayback machine) is said to archive each PDF retrieved by Sci-Hub.
http://gen.lib.rus.ec has a downloads page - (click the tab to show more options)
Torrent - books and text books - http://libgen.io/repository_torrent/
Torrent - scientific papers - http://gen.lib.rus.ec/scimag/repository_torrent/
Usenet - http://libgen.io/repository_nzb/
DB dump - http://gen.lib.rus.ec/dbdumps/
