I have a 3640 that has two ethernet 10MB interfaces. interface 2/0 is facing a public IP network. interface 1/0 is facing a private network. The private network is connected to another public BGP network. My question is can I route a public ip from interface 2/0 through the interface 1/0 to the public network that is internal.
I think you are asking whether you can tell your private network about the public ip which is located on 2/0, correct?
You could use and internal routing protocol, like ospf, to tell the other routers about that public ip so that your whole network is aware that it exists on your local router.
Please explain further if we are misunderstanding you.