Nunu is a champ that is focused on AP damage making him a great AP carry with low cd's on their harras skills, plus giving an extra advantage on teamfights for its ultimate and its Movement and Atack Speed, Nunu has a great chance at giving the Final Blow to enemies making him a good chaser for the slow.
We have to focus Nunu on carrying teamfights, he will be a great initatior for its ultimate, with the help of a good support champion or good item build he will have that role on teamfights.

Well this build will help you getting those kills plus you can get an awesome combo with the hourglass. If you dont want the Lyandri's Torment go for a Rylai's Scepter that will help you with an extra slow on casts.

Well this will help you with the fast jungle that Nunu gives you. We get our Q first to get that extra health when jungling plus deals a large amount of damage to monters allowing you to be extra fast while jungling.
The we have the E that's just another extra harras weapon will allow you to finish fast those small monsters on the jungle without wasting your Q.
Now we get our W at level 5 beacuse that's when we will start ganking, this will help you and your ally go chase to get that final hit on champions.
Our Ult is so effective when you go 1v1 with some champion or when starting teamfights, just remember to try to cast it as long as you can, because the longer it charges the higher the damage will be.

We will go for an offensive build with Nunu. We focus on AP damage plus some armor or health to help you on teamfights, plus that extra gold for our Smite.

Well for our runes we will focus on Magic Penetration Plus some armor and AP runes for late game. Our Quintsenses will be focused more on Late Game AP bonus.