Pros- high dmg, high burst, ok utility, it's hard to fall to behind.
Cons- you are squishy, so you will get bursted down easily, and if you catch some cc, its probably a grey screen for you.

Flash- gives you a nice gap-closer
Smite- we are jungling, so yeah...

Start: basic: you will take Hunter's Talisman and a Refillable Potion is just better on Nunu that 3 Health Potions as it is more gold efficient, and you don't need too much extra hp as you already have jungle sustain in your kit.

CORE: Buy these items in order from left to right. They will give you enough dmg and some utility for the team. Skirmisher's Sabre - Runic Echoes- we are going ap, so this is the best jungling item you can go for (I prefer red smite, but you can go for blue one if you want). Shurelya's Battlesong will give you some ok stats, and help you in ganking and positioning for your ult (also don't forget that it also gives ms to your teamm8s). Morellonomicon -magic pen, ap, hp, and grevious wounds, perfect stats!

Adapting- Abyssal Mask is if enemy team's magic dmg dealers are a threat. This item is really good for us as it gives mr and hp for tankiness, it gives mana which is fine (i never had mana problems on nunu though), cdr is very usefull, and its passives are nice. So 1 gives you some sustain and mana (of which neither you really need), but other passive is really nice (every enemy within 325 range of you takes 15% more magic dmg)- so item gives you both survivability and dmg out-put + it can increase your teamm8 magic dmg output when attacking an enemy thats close to you. Zhonya's Hourglass is for some armour, now I know that it doesnt give some great tanky stats, but hey, it gives what it gives, its active is great, and it gives nice amount of ap. You should get 1 item from "Adapting" when the game starts gatting rough (but finish your core first).

Boot upgrade: Yeah, you should take Boots when you have leftover 300g. (but if you finished your jg item, and still dont have tier 1 boots, buy them no metter what) Go for the Sorcerer's Shoes for that magic pen. And yeah, and Its a good idea to go for the boot upgrade after shurelya's.

Damage output: So, when you finish your core, finished boots, and already bought an item from "adapting", you should have 5 items in your inventory, all that is left is to take 1 Damage output item. Rabadon's Deathcap-Gives huge amount of ap, you want to take this when you aren't taking any of the other 2 items from this category. Hextech Rocketbelt take this when you want to finish off your build with a bit more hp. Void Staff- you want to take this when enemy team hase some mr.

You want to start with your Q ( Consume) and than take W ( Blood Boil) for clear. Than ofcourse E ( Ice Blast). You want to max E first as it is your main dmg scource, than W for ap that it gives, and than Q. Ofcourse you put a point in your R ( Absolute Zero) whenever you can.

Using your abilities: Q- objectives and jungle clear. 2 things I saw some players NOT doing and they should- 1. When at your first buff, dont start it with Q, first take like 2 hits, and than use Q; 2- During fights, if you are getting low on hp, dont forget to use your Q if there is a minion/monster near you.
W- So again for faster clear, but if you can cast it on your ally, don't cast it on yourself, and dont forget to use it when pushing towers.
E-your main dmg scource, which is great, as it is an point and click ability, you really need to try hard to miss it.
R- Well, you can use this in multiple ways, but most comonly rushing with Predator into a lane. hitting your E, and ulting while standing next to your oponents (little closer to their tower than they are, that way it is harder for them to escape both from your bot lanners, and from your ult. Usually with a tank Nunu, during team-fights, you would run into the center of enemy team and ult, but i dont like that with this build because you aren't tanky, and you could get bursted down before you even pressed R.

Predator is for a little easier ganks and for easier ult positioning.-charge it before enemies saw you.
Cheap Shot-its the best of the 3 for us, and it isnt a bad rune.
Zombie Ward- more vision.
Relentless Hunter- Helps you get around the map
Scorch- adds some dmg, but you can take Nullifying Orb If you think you'll need it.
Celerity-it has a nice synergy with Predator, and little more ms couldnt hurt + we are also taking Shurelya's and boots, so it will give you ap from that as well.

There isn't much to say about this... Think like you are playing an assassin jungler. Go gank, kill somebody, or at least make them leave their lane, and than take objectives, because of your Blood Boil, you shuld take them quickly, when taking dragons Consume does make it quicker as well. Look out to close out the game. Let's say you got a good gank on bot, and you took the drake, take your camps that are nearby, go back, and get your snowball rolling! And if you are already fed, giving some kills to your teamm8 is a great idea, as that way you will have less to carry, and if the enemy team takes you down, there will still be nice chances to win a fight if you invested gold into your allys.

Some Tips- 1. If enemy jungler kills you, and steals your buff and some camps, don't care too much, that wont set you to behind; you aren't dependent on your buffs, nunu scales well even if you died a few times early.
2. I like babysitting bot because if you get a good gank of there, force both oponents off-lane, you have a really good opertunity, with your bot laner and supp you can take dragon in no time (3 of you + Consume and Blood Boil) and tower will also fall quickly (again 3 of you + Blood Boil). What I also like about bot lane as a jungler is that when you make enemy bot lane go away, jungler can't def as easily as it is 3 of you down there, so he is most likely going to steal some of your camps, or gank some other lane (which for you doesn't metter- you are Nunu, so a few camps wont do to much harm to you, and trading them 1 kill for a tower and/or dragon (maybe even some kills) is completely worth it).
3. Always keep your eyes on the lanes, now this is for other junglers as well, but you never know when an opertunity for a perfect gank will come.
4. At the start of the game look at oponents bot and top, if for e.g. top came late to lane, that almost for sure means that enemy jungler started at the top side. Doing this will give you a nice advantage over your oponent, as you will know better where he is, than he/she will know where you are.
5. In most of the games, at 1 point you will take around 1/2hp of squishy targets, than you want to keep as much pressure as you can, constantly gank, constantly force objectives, thats how you win the game, if you stop pressuring the map for just a bit, that gives your oponents a gap throug which they can come back to the game and we don't want that.

Yeah, this build is quite strong- it has: high dmg, fine burst, fine ganks, but the most important thing about this build, its biggest + is that it is really fun to play!