On this build i'm going to show how to build AP nunu.

Starting with ice blast and Doran's Ring can help you to get fast first blood. Start with ice blast and then attack to him and use again after that he is probably running then use exhaust and ice blast. This will be lot easier if you have teammate fighting with you.

After some time you got your ulti. Nunu's ultimate is easiest to land on enemies by running to brush several enemies chasing you. Just use your ulti and they lose about 3/4 of thei hp's(or more).
Getting blue buff is good idea for nunu because you get hp with consume and attack speed with blood boil you can use ice blast too because you get mana regen from the buff.

On late game your ulti will deal about 2k dmg and your ice blast deals about 700dmg. Then just use your ice blast and bloodboil and attack if he is faster than you use exhaust and ice blast and he gets killed.

Nunu can get assist very easily just use bloodboil on your ally and if he kills and enemy you get assist.On teamfights always use bloodboil on your allies.

Pros:
- Very high dmg
-Can kill 2or more gankers with ulti
-Consume is good on jungling
-Blood boil gives you 55% attack speed on max lvl.
-Great ganker

Cons:
-If enemies buy magic resist bad
-Silence is very effective to nunu