[user5994461]

It's trivial: use a couple of USB external hard drives.

You don't want to deal with cloud on a home connection, it's gonna take forever.

If you are a company, you pay for storage on S3, Google Storage, OVH or IBM Softlayer. It's great quality yet simple and moderate costs.

Companies keeping data in house pay for NetApp, NetBackup and tape hardware.

[ams6110]

Even with USB it's going to take many days to back up 17TB.

[user5994461]

These kind of stuff support incremental and differential backups.

[NikolaeVarius]

You should have started the backup process well before you hit 17gb of data.