Can you use three Cyber Dragons and three Proto Cyber Dragons in a Yu-Gi-Oh deck

Yes you can. Proto-Cyber Dragon is only treated as Cyber Dragon when it is on the field.

This is different than Harpie Lady 1, Harpie Lady 2, Harpie Lady 3, and Cyber Harpie Lady that are treated as "Harpie Lady" all the time and thus you can only use a combination of three of these cards per Deck and Side Deck combined.

It is similar, however, to the Harpie Queen ruling. Harpie Queen is only treated as a "Harpie Lady" when it is on the field or in the Graveyard. It does not specify that it is always treated as such. Because of this, you can have up to three Harpie Queens and three Harpie Lady combinations in your Deck and Side Deck combined.

It is important to note that as of the March 2010 Forbidden/Limited Card List, Cyber Dragon has been Semi-limited. Therefore, a player can have up to two Cyber Dragons in their Deck and Side Deck combined.