You could always use Amazon S3 and store whatever you want in there (size and content doesn't matter)... Also
DigitalOcean Spaces is similar service with easier pricing structure (and probably cheaper but might not be more redundant)...
This is what is called "object storage"... The only downside of this is that you can't preview stuff (no thumbnails in folders etc) you can just upload files to it and download them back once you need something...
Other also good idea is to buy a cheap server with drives in RAID and just upload data in there. There's also a free cloud software, similar to Dropbox with it's own cellphone app for iPhone/Android, desktop clients, full user administration etc... It's called
OwnCloud that you can install on that server that you can manage your own cloud.
Third option are Google Drive/Dropbox but you would have to check their terms to see if that's allowed. And even if there's nothing against it - they might say that it's not appropriate etc... Only if you would use Dropbox Business they might probably be fine with it...