I've seen a few AP Kog'Maw builds but I think mine is unique, and personally, works best for me. This is my first guide so please bare with me! Kog'Maw as an AD carry typically does high amounts of damage very quickly. I don't play him as an AD carry because tanks expect it all too often. When you first get the void staff it's just too late, you already have an attack speed of 1.5+ and each attack with malady will be reducing there MR anyway. When finish this build can do SERIOUS damage in a very quick amount of time.

Pros

High damage Output
Deadly Range
Will drop Carries MR into the negatives BEFORE added MP
Can drop 90% of enemy champions in 1 on 1 matches

With this being said, the cons are sometimes frustrating

Cons

Must be conservative with mana
Terrible escape ability(Though you will do fine if careful)
Always squishy
Must be played passive-aggressively until mid-game
Slightly reliant on skills(Short-Cooldowns though?)

Why malady first?

Reduced MR, higher attack speed, little more damage on your Caustic Spittle and Void Ooze.. It's what AP Kog'Maw needs!

To be quite honest, I actually never use Sorcerer's Boots, since void staff is all I really need as far as mage penetration goes(Plus Runes). Since Kog can already lower mage resist with his Q, I'd rather use Boots of Swiftness or Mobility depending on the range of attack on enemy champs.

Rabadon's Deathcap is pretty obvious, the damage is nice. You could go with Nashor's Tooth first for cooldown and to make it a bit easier on your mana, it's really up to you.

Mejai's soulstealer, Could get it earlier but the assists and kills in team fights(If things are favorable) Make it a viable item without having to wait to have 3000 gold.

That's it for items I guess, Ryali's Sceptre is also a good item. Otherwise I don't change my items much. Hp is kinda useless, you're meant to be squishy and meant to stay at a distance. Can't change destiny.

Caustic Spittle Vs Void Ooze

Which comes first? --> This is the only part I have trouble with when playing AP Kog'maw.. This is a question that will probably haunt me forever, and this is why..

Void Ooze, BIG mana drain BUT, by the time you have void staff and Void Ooze to level 4 you can farm SO much easier. Greater slow with higher levels, so when you get your Living Artillery this is a great help. Being that in this build I get boots later a higher level and longer range from my W helps A LOT when chasing down opponents.

Caustic Spittle, faster attacks, and will decrease your opponents Magic Resist and Physical resistance. The difference between 2 levels in this skill is 10% quicker attack speed and a null in 10 points in opponents defenses. This skill will also, in a way, passively make your W more damaging. Decent Cooldown, short enough to do a good majority of damage

Your W! I'd recommend only 1 or 2 levels before level 11 as for each 100 points of ability you have will equal another 1 percent of opponents hp on top of whatever the opponents mage resist is after malady and void staff kick in. Only thing missing is the range, but with the increased slow from void Ooze you can do without the range.

Not much to say here, you could put more points in offense and personally I don't even use the blue buff so.. The preference is yours.

Good thing about this build is Kog is fairly versatile in terms of runes. He needs mana, so mana regen or extra mana is not bad. Neither is attack speed, Ap or Mage pen. Anything along those lines will more than likely work well with this build.

Ignite for people who like to heal, and I've had more luck with Ghost than flash, since you get more distance. His escaping ability is bad, but if you have some distance already your slow will help IMMENSELY. If you're still paranoid or dying too much, I suppose you could try Heal or Flash. Again it's all preference.

Few Tricks that are probably obvious to everyone but..

I've played AD Kog'Maw's with this build, and this build is much better in my opinion. The fact that after malady kicks in on most carry's, there MR is literally negative and I couldn't even imagine what it is after mage pen. Void Ooze and Caustic Spittle deals 600+ damage each after a few hits. Factor in my W Other champions melt, even most tanks.

Perhaps not the most detailed guide, but I will be watching and adding to this guide as I have yet to find another champion that is so unique and.. Dangerous.

Hope I've helped!