Hi,
It is very much like other protocols will consume memory for storing the routing information and to store info. used to send and receive the same. Simply said, it needs memeory to save neiboring and topology table info.
Bytes consumed for a single route is bit difficult to tell, but you can calculate the same using the EIGRP Packet format.(Look under EIGRP Packet Format)
http://www.oreilly.com/catalog/iprouting/chapter/ch04.html
Rate if it does,
Rgs