The MyCloud is a Debian Linux computer. At least some of the 56 gigs is the operating system.
Logging out? Via web? Is there not a log out link on the page?
Or are you accessing via “My Network Places” or similar? There isn’t a sign out then, but there is a “disconnect” of sorts somewhere, but no real need to to that… However, the mounted drive usually saves the user on first connect. You need to refer to your computer’s operating system instruction on how to handle network drive connections/disconnects.