First of all I want to say that I started to play Kog'maw has a pure AD. Using malady, wit's end and Madred's Bloodrazor to deal quite insane damagies. This build is to open another path toward another game-play. Even if it can quikly blow up your mana, some AP can make caustic spittle and void ooze turning into deadly attacks.
Of course Living Artillery would be a master piece of the game play but it won't be the most deadly spell.

In many builds, Kog has laborious starts. It won't change this time. So Runes won't focus on flat AP.

3 Greater Quintessence of Potency will be enough to start the game.

First of all, I use 9 Greater Mark of Insight for magic menetration. The point is not to make additional damages with AP... It must reach the enemy HP pool.

During your first lvl, save your mana. Your AP will grow with 9 Greater Seal of Force and your improved skills.

A problem will be that your mana will be vaporised... Use 9 Greater Glyph of Clarity to get your mana back faster.

Nothing special to say. It's the common masteries tree for a caster. And now your Kog is ging to melt your enemies with it's magics attacks.

To start with Kog, you'll need some survivability. Personally, I run with boots of speed and regent with 3 health potions. It allow you to make early harassment or to survive in lan if you oposent is not kind with you.

To make your farm easier and improve your late efficacy, you'll need the Berserker's Greaves. To acti in synergy with your base attack and your Bio-Arcane Barrage.

You'll now need some AP, some mana regen and to shorter your countdowns. Get an Kiendish Codex.

The monster has to increase his destruction power : use a Guinsoo's Rageblade.
You'll start to get a pretty good burst and an impressive hability to finish fleeing enemies.

Then upgrade your Fiendish Codex into a Nashor Tooth. You'll improve your attack speed and you'll cast more often.

In order to reduce the nomber of recall, I have chosen the Hextech Gunblade.

The tow last items are up to you. It will dramatically depend on the situation.

If you are facing huge Hp pools, take Madred's Razorblade.
If you are facing some trubles with casters take the Banshiee's viel or an End's wits.
A Rod of agies can give you some HP as well... But prefer a good localisation if team figth. you have a huge range. Use it!
Against Magic defence you can use a Void Staff.
Feel free to adapt you end stuff to your enemies. It may change the team-fight end.

This build use Bio arcane barrage to finish fleeing enemies. It won't be a priority.

The attack sequence is to cast at first a caustic spittle to decrease resistences to the followings spells, and simultaneousely cast Void Ooze and Living Arilleriy. Try it and you will never see Kog the same way again ^^

Void Ooze and Living Artillery will allow you quite early in the game to two shot a creep wave and quikly push a line or to maximise your income.

Make sure to use your Void Ooze to slow down your prey, to escape or to save an ally.

Using Living artilllery and Void Ooz when you flee can be deterrent they don't want to finish low life in your jungler territory or in front of another ally in late game.

Kog'maw has a fearsome lack of way to disengage close combat. Flash is generally capital for me to save my paper-made ***.
So be really carefull about possible ganks or rushers like Lee Sin, Xin Zao or Akali.

A second problem problem you will face is a lack of mana. Make sure to get a blue at the right time. Otherwise you'll have Clarity. But be carefull. You can easily vaporise your mana pull in no time^^

Make sure to stay away to the brawl. You have absolutely no resilience. One defence could be to wipe an enemy before he reach you.
But be sure that you have the upper and in range. Over-use it!

Use your ulti to scout the grass all around you to avoid you or your team to be gank. You can use it as well to check important neutrals like drake or nashor without make you going in dangerous areas.

Thanks for reading.
I hope that you got some help from this guide and that you got at least the curiosity to test an uncommon way to play Kog.
Thanks to coment If you like it or if you have constructives remarks.

Have fun! ;o)