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 is said to archive each Sci-Hub query.
http://gen.lib.rus.ec has a downloads page - (click the tab to show more options)
Torret - http://libgen.io/repository_torrent/
Usenet - http://libgen.io/repository_nzb/
DB dump - http://gen.lib.rus.ec/dbdumps/
