Like Bunny Tracks said, Archive.org. If you want tips on how to archive videos yourself, you're going to have a hard time archiving terabytes of data. It's going to cost you hundreds/thousands of dollars in hard disks/optical discs/other storage mediums.
The cheapest way at the moment would probably be to buy a blu-ray burner and several hundred 25GB blank discs (25GB discs are pretty cheap compared to larger capacities). After the initial cost of the burner, the discs are cheaper per-GB than other storage mediums and are easier to store and more reliable than hard drives (both mechanical and solid state drives have issues for long-term storage.)
There are also "M-Disk" blu-ray discs that are engineered for extreme long-term storage (as in hundreds of years). But those are several times more expensive than regular blu-rays.
The blu-ray solution has it's own issues (discs with larger than 25GB capacities are pretty expensive, having the data spread out amongst multiple discs is really inconvenient when you want to access things, discs need to be stored correctly away from sunlight and moisture, etc).
Even doing this you'd only have a local backup of the videos, though. You're better off seeing if you can get archive.org to archive the videos.