Hi and Welcome to my first and only ( I think ) build :) Which I am focusing on building Wukong as a damage dealer Champ :) , Plz Try it out and write a comment what you think!

During the chaos of the Rune Wars, an enormous runestone was lost deep within the Plague Jungles. It remained there, untouched for centuries, emanating a potent magic which infused nearby wildlife with sentience and vitality. A group of monkeys who were particularly empowered by it came to worship the stone, and their leader - a wise sage - became convinced that he could harness its power to make the monkeys immortal. He performed an elaborate ritual, but things didn't go as he expected. The runestone was destroyed, and instead of granting immortality, it produced Kong, a monkey who carried in his heart the strength and power it had contained. Kong was driven by an unquenchable desire for greatness. He sought out every beast and monster the Plague Jungles could offer, eager to find a worthy opponent, but none offered the challenge he craved. He asked the sage for advice, and learned about a legend of hairless monkeys to the north who, with wits and might, had bent the world to their will.
Wukong left, journeying north, determined to discover if the legend was true. He crossed the Southern Wastes and then the Great Barrier. On his way, he happened upon Master Yi, who was deep in meditation. Kong asked him who the strongest warrior in the north was, and Yi told him about the League of Legends. The tale intoxicated Kong, a place where he could battle the strongest fighters in the world was, to him, paradise. Kong asked Yi to introduce him to this League, and to teach him the ways of humans, so that he could be a fitting champion. In return, he would honor Yi by using Yi's Wuju style to become the greatest warrior Runeterra had ever seen. Admiring his passion, Yi agreed, but under the condition that Kong would one day teach the lessons of Wuju to a pupil of his own. In the spirit of this agreement, he renamed Kong Wukong, and gave him a weapon suited to his unusual nature - an enchanted staff that the young Doran had crafted. The weapon was an unrivalled masterpiece. Guided by Yi, Wukong joined the League of Legends to prove himself as the best, and to show the world the true power of Wuju.

"Only in combat do you learn who you truly are."
Wukong

Well, first of I have loved the tale of Sun Wukong, a long time. My favorite movie is The Forbidden Kingdom which Monkey King (Wukong) Is in ;) and I have even read Dragonball which the main character Goku is based on Wukong. So when I first heared about the release of Wukong, The Monkey King I got really excited and I have played him alot since he got released ^^

Anyway I like playing him because he has a great burst damage, and his gorgeous ultimate Cyclone ;)

and not to talk about his Warrior Trickster skill. Lets say, you getting chased by a Caitlyn you got 100 hp left and she put on her Ace in the Hole on you. Not a problem just Warrior Trickster and the Warrior Trickster will save you :) perfect!

I have made some changes on both Build you find below what I have changed :)

Build 1 Original: Changed the Warmog's Armor to a Frozen Mallet instead because like Mikuroo wrote: "one of the few things I would like to point out is you may want a Frozen Mallet for the slow". It is some less HP but it gives you 20+ Attack Damage.

Build 2 Mega Damage: This is the one I have changed most on. I updated the runes to a bit more "Serious" runes. So instead of going raw damage I have changed to.
Greater Mark of Desolation Armor Penetration Marks.
Greater Seal of vitality Because this build focus mostly on damage so it is always good with some extra hp.
Greater Glyph of Attack Speed To have some few extra % attack speed.

I also changed the skilling order a bit.

I have chosen this types of runes , I like it , but feel free to have which one you like :)

Greater Mark of Desolation Always nice with some Armor Penetration ;)

Greater Seal of Armor Always good with some Armor this runes

Greater Glyph of Scaling Magic Resist in Late Game you wil always need so much magic resist as possible against those magicians! so I go with Magic Resist per level! This runes + Greater Seal of Armor + Stone Skin Gives you a really nice amount of Armor and Magic Resist early game too.

Greater Quintessence of Attack Damage I choose this type of runes to have some attack damage early game I used to have armor penetration quints but I like Attack Damage better.

Not much to say here ^^ , I go alot in offense to get some extra damage on minions 3% extra lifesteal more damage per level and stuff like that, and only 3 in Defense with some armor.

As you see I pick Exhaust and Flash I like them alot! Flash for some nice chase or escape and Exhaust to easy kill enemies, chase, escape etc. But sure other spells works fine too.

Ignite: Its a great summoner spell too. versus an ad Sion which try kill you thanks to his mega super Lifesteal This Spell will make him cry! its also a great counter against any fast health regeneration champions like Dr. Mundo or Volibear

Heal: Always good with some heal! ;)

Ghost: Is also good on Wukong if you want to chase or run away from champions.

So as you see I max Nimbus Strike first, Actually it dosent matter which one you max first I just like it better to max out Nimbus thx to the attack speed you gain. But its great to max Crushing Blow to , just dont max Warrior Trickster right away x)

I start of with a Doran's Blade it's a great first item because you are kinda squishy which give you +10 damage +100 health and +3 Lifesteal. If you don't want to buy one, its fine to start with a Boots and 3 Health Potion.

I then hurry up and finish my Ionian Boots of Lucidity its great with some Cooldown reduction especially your Cyclone. If the team have some Heavy CC just buy a Mercury's Treads And you will be fine.

After I have finish my boots I buy a Sheen. Sheen is a really great item on Wukong. Because it work with Crushing Blow! So u can just Attack first with Nimbus Strike Proc Sheen and attack with Crushing Blow to deal a "tons" of damage and come away safely with Warrior Trickster

I then after build a Phage its a great item which give you some nice amount of health and damage and the passive: Your basic attacks have a 25% chance to slow your target's Movement Speed by 30% for 2,5 second!.

Later I Build Zeal for some nice amount of attack speed, crit chance and movement speed. Then finish Trinity Force To gain all Sheen, Phage and Zeal attributes but even better! :)

I usually Build a Bloodthirster after the Trinity Force by first buy a Vampiric Scepter and then after B. F. Sword and then finish it to a Bloodthirster This Item is really great and making your Ultimate Cyclone making such great damage that the enemy team should start fear you alot. Sometimes if I feel like to have some more health I build a Warmog's Armor first.

After I have build Bloodthirster and a Warmog's Armor I usually build a Atma's Impaler

This Item do really shine! It gives you armor and Crit chance and even the godlike passive: Physical attacks deal an additional 2% of your max Health in damage. Which is super great! Your ultimate Cyclone Will now really shine! The Enemy team will now really run in fear when you charge at them! :D

The Last Item I have put in the Last Whisper is a really great item it gives you 40% armor penetration its really great against tanks. Last Whisper + Cyclone = "Tons of damage" But you can actually build whatever you want in the last slot of your "bag" If you want some more armor like maybe a Sunfire Aegis or more damage like a Infinity Edge its fine :) just see what the situation is on the match and feel free to build whatever you want!

Well so this is the end atm :) I will try update this guide as much as possible (If it will get popular ofc) So plz Try it out before comment something stupid :) So God bless you all See ya!