"The cloud" is just a term for "somebody else's datacenter", and it's filled with honkin' big compute resources as well as data storage.
Some of the contract work we and other defense contractors do requires compute resources beyond those we can readily place on-premises and maintain in a cost-effective way for short-term use (a 1-yr contract for example). So we make use of AWS GovCloud compute capabilities. Some data storage is involved, of course, but it's typically just that which is directly tied to the compute instance.
The security aspects of any datacenter are real, and nothing is absolutely, perfectly secure, but the concerns are adequately addressed by both Amazon's (AWS) and Microsoft's (Azure) datacenters, at least to the government's satisfaction, and thus to ours.
Among many other things, the "GovCloud" datacenters are manned entirely and exclusively by U.S. citizens who are thoroughly vetted. The physical access and network security surrounding those datacenters is outstanding.