i created this build to show people that nunu dont need to be a tank but an full nuker.

i choose flat ability runes to get get good early game.
cooldown quint for to get your ulti faster
and magic penetration for it to hit harder

i choose to get the utility tree to get the cooldown reduction at the end and some more ability power and armor

doran's ring: i tried other tings but dorans ring gives the best start because u get both ability power an mana regeneration and 100 HP as which makes u stay in lane more.

sorcerer's shoes: is the best shoes for a nuker because with 20% magic penetration u hit thorugh their magic resistens and hit harder

mejai's souulstealer: is the item that gives most AP after rabadon's deathcap.

nashors tooth: to get your free-spells from your passive and a bit AP and cooldown-reduction

lichbane: because if u slow the enemy u run over and hit them :D

rabadon's deathcap: to get a big AP boosts.

banshee's veil: to protect u from CC when using your ulti.

the sequence is R-E-Q-W
E 1st because its your main killer skill
Q 2nd to restore your HP or good with lichbane
W 3rd to it is great when u used E, u toggle it on and run up and bang they are dead

clarity: to restore your mana if needed

ignite: to do the last dmg on the enemy so u dont need to tower-dive

thornmail: if enemy are heavy dps u can switch out banshee's veil or mejai's soulstealer if they got much CC

morello's evil tome: if u didnt get a good start and dont got too many kills, u can switch it out with mejai's soulstealer

force of nature: if they are heavy AP

Zhonya's hourglass: if they hit hard from both AD or AP. switch out with banshee's veil.

use E to slow them and toggle W and hit with noral att and finish with R
if u lose alot of life then use Q on minion