Where is the proof he was influenced by Joe Budden other than a throw away comment he's made about 20 other people? I don't hear it and did he influence Drake or the people actually writing the rhymes?
Telling people you fukk with their music is one thing. To act extra with it, almost like a goofy fan, is over the top for anyone that is a serious MC. Now in hindsight I can tell he doesn't take MCing as serious as a lot of other rappers do since he doesn't write his own rhymes but that is another thread....
Fam, if you expect me to post a text book for you to research, I'm sorry but it doesn't exist. What I do know is how culture and influence works. Drake came up during a time when Joe was a very popular rapper amongst underground/ lyrical internet heads.
If you want proof that Drake was influenced by him, really sit down with Joe's first album and his mixtapes that came out up until the time when Drake first hit the scene, and the answer will reveal itself to you. I'm not saying Joe was his only influence by any means, there's also Phonte, 'Ye, and many others, but Joey's influence is obvious.