"Security" and "cloud computing" are mutually exclusive. Anything the military wants secure should never be near anything that touches private cloud servers. Just in the last week, there have been reports of two massive breaches of security made possible because of supposedly secure data being on cloud servers. If you store data on somebody else's system, it is NEVER secure, nor is it even entirely yours! If the data you want to store isn't sensitive and doesn't need high security, that might be fine.
Anything the military is storing could be considered sensitive, even if only because you could track ongoing/completed but still classified operations through the time stamps of otherwise innocuous data, just as one possible example. Then again, the modern, most ass-kicking military in the world can't be bothered to properly maintain all ships and train all personnel to avoid things like naval ships ramming other ships, killing some sailors in the process, so why would they care about the small issue of data security?