Typically, high damage, range and sustain with hp-based scaling damage can turn a tank to a wimp.
Especially in ARAM.

Personally, (Yes, this is strictly my opinion) I could not play AP Kog'Maw well enough to be good at it.

This build and Kog'Maw's kit together is a counter to counter-building.

Blade of the Ruined King: Attacking full-hp champs is easy harass especially with Kog'Maw's W.

Berserker's Greaves: More attack speed and mobility for a marksman.

Wit's End: Reason for using this before Nashor's Tooth is simply because you want some
early durability with some actual shredding. Wit's End STEALS Magic Resistance per hit, boosting your damage.

Nashor's Tooth: Finally some cool-down reduction, more attack speed, and more on-hit effects to further boost your damage. Passive synergy is almost TOO good. IMPORTANT CHOICE: 60 AP boosts your W by a FULL 1 percent, due to rounding. This is practically a free 40 AP that you don't have to buy.

Infinity Edge: This finally stacks more damage for your life-steal to be even more effective, with boosted critical hit power.

For the final item, explanations for each choice:

Sanguine Blade: If you really need the life-steal and you are not challenged by ignites or grievous wounds, this is a good item to pick to last through team fights. With near max attack speed, the stacks go up pretty quickly.

Trinity Force: This would be my choice if you really need to end the game. Kog'Maw's cool-downs are short enough along with Nashor's Tooth to consistently use Spellblade procs.
None of Trinity Force's stats are wasted.

Black Cleaver: While this item does not add to attack speed, it can work well enough to gimp Armor stacked teams, along with the previous items already doing magic damage, this should be the least likely choice, enemies are basically forced to build MR if they review damage received when they are dead. But, this does provide more health, CDR, damage, and penetration.

Caustic Spittle: This ability's passive is good to further empower your build as it shreds armor and magic resistance. It's not TOO important early, but do not leave it for the last 5 levels to max as enemies do build more resistances, this helps combat that.

Bio-Arcane Barrage: Max First! This ability is so powerful against enemies buying any form of health and not resistances. As a marksman, you need the extra range to poke and sometimes even getting those final hits on fleeing champions.

Void Ooze: This is your CC. The slow effect is adequate enough to punish anyone without a gap-closer or hard CC that advances on you. Lay this down, activate W and unleash some attacks. Another strategy for this ability is using it when enemy team jumps an ally, this can hold enemy team in a spot for your team to hold enemies down for you to snipe like a good marksman.

Living Artillery: This ability is pretty great, just do not burn your mana spamming this. Use as follows: Against a cluster of enemy champions, to poke as you retreat along with your E slow for better accuracy, and finally to deal extra damage 1v1 against an enemy champion. Keep in mind this ability has its own steroid of boosted damage against champions.

Marks - Attack Speed
Why? Late-game, you will depend on on-hit effects, the more frequently you can attack, the better the result.

Seals - Armor AND Glyphs - Magic Resistance
Why? This will save your life A LOT of the time in skirmishes and 1v1's, having some durability never hurts. (It just makes things hurt less)

Quintessences - Life Steal
Why? This boosts you from having no sustain, to better sustain when completing your Blade of the Ruined King. After obtaining your Infinity Edge the life-steal will make a stronger difference.

I do not have any skins for Kog'Maw just yet, so I kept the classic so I do not feel like I cheated on you readers.

Please post any suggestions, comments or even results (GOOD OR BAD is ok here, we can learn from these and further change for the better.)

Do not forget to vote if you liked this build.

Good luck, Summoners!