So this started more as a test build to see if Warwick could hybrid seeing as his abilities work well with AP, as you can see with Magewick, and his auto-attack uses AD [Obviously]. This actually work surprisingly well, though it is fairly expensive and you pretty much have to do it jungling seeing as you don't get enough gold in lane unless the other team is feeding.

Anyway to make this work you're going to have to jungle, I usually start by taking out the two golems near Lizard buff using smite on the first one. After that move to the wolf pack and kill them with hunter's call, and hungering strike, then move to the wraiths and take the blue one out with smite and killing the rest with hunter's call. After this depending on how long it took the two golems should be back up again, kill them. Move back to wolf pack then to Golem buff, make sure to save your smite for the golem. If you have enough health or have already gone back to get Bilgewater kutlas kill the dragon, as it will net you a decent amount of gold. After this head back to the wraiths then to lizard buff and you should be lvl 6 by now. Which means gank time.

For ganking I usually go for the lane that was left solo since the person on your team in that lane should be at least lvl 6 and have their ult ready for a gank. After that if you kill one of them stay for a bit to see if the second over extends or if you kill both push the turret using hunter's call. After that if you got turret or if you failed to kill anyone but are still alive continue to run around helping the middle top and bottom lanes. Try to keep the mana buff as long as you can unless someone else on your team can use it more effectively. During the ganking phase you're going to want build your Merc treds and your first Hextech Gunblade.

Once you have your first three items the rest of the build is pure necessity. If there's a lot of CC get banshee's if they're tank is doing well go black cleaver or possibly last whisperer. If your team is pushing well and you feel confident go for another Hextech.

Now the reason I don't have a IE or BT is because quite frankly they're not as good as hextech. Hextech is going to make hungering strike and ID far more effective than normal. The life steal and spell vamp also work very well with his auto attack especially with hunter's call giving you 80% AttSp increase.

Anyway enjoy the build it's very fun and please don't vote up or down unless you actually try it out. Also this build is not for everyone.

EDIT: For Some reason my summoner spells are not showing up but I chose Ghost and Ignite, Ignite for jungling and Ghost for chasing/escaping.