Hi there all and welcome to my first build.
I hope you like it and please do comment if you have some suggestions ;)

Mid lane

Some other builds already suggest to go mid with Corky. I do like the idea and also recommend going mid, but it doesnt mean you cannot lane with Corky! Depending on your team setup and the opposing enemy on mid, you might want to switch with someone who could be better on mid.
If you lane propperly, farm a lot and clear the jungle sometimes you might even keep up with mid.

Farm

I think we can all agree that Corky is the master-farmer. But none of the other builds ever suggest buying a Tiamat. Try to get that item asap (along with Boots), after a while you will see why i like it so much ^^.

The Jungle

Lots of players forget to use the jungle to their advantage. When Corky hits lvl 6, you can practically clear the creeps on mid in 2 shots ( Phosphorus Bomb + basic attack on the blue one). If you take the lane next to the gollems, do kill them everytime you pass by. If you dont take mid lane, i recommend this lane next to the gollems. Here you can get your gold from the gollems and take the red buff whenever you need it. (btw red buff is Corky's buff! use it)

Early game

For starters, what do you need more than some health regen and some mana regen? As you are a farmer, you need to stay in lane as long as possible. The health regen + pot give you some survivability.
As you will use that Phosphorus Bomb a lot on minions as on champs, you will be oom pretty soon. When you are oom, you can just shoot some minions, play defence and make sure you can always get away! Your mana will regen faster than theirs so dont just return to base as soon as you are oom.



Second item will always be Boots. If you have enough money on your first recall, try to start building that Tiamat.
I chose to build Ninja Tabi boots mainly for the early game speed. They are cheep as hell and will give you a nice advantage early game.
____________________________________________________________________________________________

Mid game

As you have been farming and killing some creeps, you now have enough money to buy that Sword of the Divine. It gives you a significant amount of attack speed and bonus damage on every 4th attack.
Dont forget about his active, it will give you some extra ArPen and make you undodgable for 8 secs. I suggest you spam it against jax, as he will do bonus damage for every attack he dodges.
Get yourself that Infinity Edge, the AD + CritStrike will help you win your battles.
____________________________________________________________________________________________

Late game

Bloodthirster for extra AD and some lifesteal, Trinity Force for some overall improvements.
If you are dying to often on late game, concider buying some defence. This build is mainly made to nuke your enemy, but you cannot nuke when u are dead. I suggest you replace Tiamat with some defence on late game as you wont need to farm anymore.
Also replace your Boots and buy Merc Treads!
If you feel like your enemy is always getting away low hp, get a Frozen Mallet, spam ulti and slow them to take them down.

Take Phosphorus Bomb as first skill. With it you will be able to do some great damage early game.
Second is Valkyrie, this is your getaway skill. Together with Flash you can jump from midbattle right to your turret.
Try to max Phosphorus Bomb first, then Gatling Gun and as last your Valkyrie (upgrade ulti whenever possible).

Mark

For Mark i take the Greater Mark Of Desolation for its armor pen

Seal

For Seal i take the Greater Seal of Health for some more early game survivability

Glyph

For Glyph i take the Greater Glyph Of Replenishment for some more manaregen early game

Quintessence

For Quintessence i take the Greater Quintessence of Desolation for more armor pen

-- Use your Gatling Gun propperly, try to keep your enemys in range so their armor can be shreaded!

-- Spam your Missile Barrage, early game on minions to farm and push(cheaper than Phoshporus Bomb), mid game on minions, creeps and champs, late game: champ champ champ!

-- Whenever you see enemy minions breaking trough, use Teleport to the nearest minion/turret and take them all out with Gatling Gun or just basic attack ( Tiamat + Sword of the Devine will make you kill minions faster than the turret)

-- In team fight, when you are low hp and think of recalling, dont instantly choose that option. Retreat some, stay behind minions/champs and start spamming that Missile Barrage towards enemy champs.
However, when there is a kartus/nocturn or whatever champ whom can easily kill you on the enemy team, DO RUN! Not straight trough the lane, go into the jungle to avoid attacks like ezreals ulti.