Comment by wongarsu
And plenty of datacenters will be happy to give you some space in one of their racks.
Not wanting to deal with backups or HA are decent reasons to put a database in the cloud (as long as you are aware how much you are overpaying). Not having a good place to put the server is not a good reason
A DC near me that publishes prices (most don't) advertised a full rack for 600€ per month, including internet @ 20TB/month @ 1 Gbps, and not sure about the power, if anyone's curious about the ballpark cost.