Warning!!! Doing an apt-get for any Linux module has the strong potential to break the My Cloud OS/firmware or outright brick the My Cloud due to the use of 4k page system within certain My Cloud versions and firmware’s.
Most NAS, even though Linux is underneath, are a light version of it vs a full blown installation. Some might even be customized. Nevertheless, for Linux gurus (which I am not!) and those willing to give it a try, it is not impossible to build your own packages. The mycloud comes with Debian wheezy.
So you might have two options, search to see if someone has a Calibre package built for mycloud already, or build your own: