If you deal with videos professionally and need to be in constant collaboration with clients and colleagues, Google Drive can’t be beaten to backup videos. Its integrated file sharing option is a breeze to use, and all you or anyone you share your files with requires is a Gmail account (and let’s be honest here, who doesn’t have a Gmail account these days?).
BackBlaze doesn't have an offline component, so you'll have to handle that yourself, but it's by far one of the most affordable options on the market. Accounts are $5/mo (you get a break if you pay up front for one or two years), and you can add more computers to the same account for another $5/mo. You can read more about Backblaze's pricing options here.
The next page will show a list of all Google products associated with your account whose data can be backed up. All of them will be selected by default, so make sure to unselect all and select only youtube. An easy way would be to untick the "Select All" button at the top which will unselect all items. Then scroll down and check the "YouTube" option.