I saw a lot of posts here and didn't find an answer. Let me explain. I have a site and a facebook page facebook . com/example . com. In website there is a like button for each page, so users can like example . com/page, example . com/page2. So I don't know if it is possible that when a user like page1 that this like increases like on facebook .com/example . com> page? So resuming :
facebook . com/example . com has 2 likes.
example . com/page1 has 1 like.
example . com/page1 has 7 likes.
I would see on facebook.com/example.com on middle left 10 likes. Is this possible? If yes how can I do it?
It is not possible, because every like button "likes" only one object. And there is no object hierarchy so that one object would consist of many other objects or one object accumulates the likes of other objects.
What you could do is to put a like button for your facebook.com/example.com page on every website. But in this case every like button shows the same like count. Then you can subscribe to the edge event with the javascript api and count the like-button-hits on every website: http://developers.facebook.com/docs/reference/javascript/FB.Event.subscribe/
This allows you to display a counter for like-button-hits on every website but you are not allowed to display it as a facebook button.
Another solution would be to put different like buttons on every website and fetch the like counts with the facebook Graph API http://developers.facebook.com/docs/reference/api/. The sum could be displayed on the facebook page, but again not looking like an usual like count.