This is my straight AP dps Rumble build.
This build focuses on max burst aoe dps, and cooldown reduction to assist in that. This build will shine the best as a ganker. The CDR is to ensure your ult is always off cooldown when you enter a team fight or gank situation, also to ensure you can put out the maximum amount pressure via aoe dps and slows.
While Rumble has a LOT of tanky-ness to him, I have found straight damage a very successful build. His shield end game absorbs around 600+ damage, which is a good chunk to help with the tanky items he is lacking.
For Marks and Quints I chose the standard magic pen, and for seals and glyphs AP. Rumble has some amazing early ganking potential if you take Electro-Harpoon at level 2.
Again this is a straight dps guide, so no survivability runes. With the way his passive works, cdr isn't as important either as you will just over heat faster. Your boots will be enough to handle that.
For masteries I went 21/0/9. Avoiding as much physical masteries as possible. Picking up improved Exhaust and Ignite as those are the summoner spells I use, and honestly there wasn't many other choices. While Atk speed is mostly useless, it'll help while you're over heating to deal extra magic damage.
I didn't go defense as my second tree as just a few points won't make much of a difference without the glyphs or items to back it up. So I went Utility, less time dead is more useful than it looks, and taking the experience bonus.
On almost every toon I play, it's boots and 3 health pots off the start. It helps with the early ganks, which i'm all about. The boots I upgrade to depend heavily on the team I end up facing. The 3 boots listed are the best options to choose from, depending on what is needed the most. So try to have enough gold to grab your upgraded boots and your Mejai's your first port back.
After that I start building my Rylai's, which is amazing for giving you a little more early survivability, and slowing down entire groups of champion's with your Q. From there it's the standard Deathcap, Void Staff for the magic pen (you can sub this for some spell vamp if they aren't really using any MR) and finish it off with the hourglass. I chose Hourglass as my last item because by this point they will realize how ridiculous you are and start focusing you down in team fights. Seeing as you aren't very tanky and need to be in melee for your Q to work, that is a big surprise for them and will still allow you to do damage if your Q is shooting flames while you're not taking damage.
Rumble has a new resource system called heat, where he gains heat every time he uses an ability. At 50-100 you gain bonus damage to your abilities, and at 100 your passive kicks in, silencing you for 6 seconds and adding bonus magic damage to your attacks.
Junkyard Titan (Passive): Rumble's abilities generate heat. When Rumble is above 50 heat, he is in the "Danger Zone," causing all his basic spells to have additional effects. When Rumble reaches 100 heat he overheats, silencing himself and causing his physical attacks to deal additional magic damage. Rumble loses heat over time.
=This is his new resource system, it's really fun to use, but is hard to keep track of in group fights. The bonus magic damage at 100 shouldn't be over looked, but it's best to stay in 50-100 if possible.=
Flamespitter: Rumble torches the area in front of him with his flamethrower dealing damage to all units in a cone for several seconds. While in the Danger Zone, this spell deals additional damage.
=This move is a beast. Don't under estimate the damage this sucker can do in a group fight while in the danger zone. Especially combined with exhaust, your ultimate, or a different characters disable. This move is also recommended to use right before you pop your hourglass so you're still doing a large amount of damage.=
Scrap Shield: Rumble creates a shield blocking incoming damage for several seconds and granting a short duration speed boost. While in the Danger Zone, the shields strength and speed boost increase
=The speed boost is very short, 1 second. It can still be useful at max level for chasing, more importantly for keeping people in your Q. The shield gets really beast at high AP levels, more so in the danger zone. It's saved me numerous times from abilities like Karthas and his ult.=
Electro-Harpoon: Rumble launches a projectile that deals magic damage and applies a stackable slow on the target. A second shot can be fired for no additional cost within several seconds. While in the Danger Zone, the damage and slow percentage is increased.
=A skill shot slow, which gives you a free second shot. Amazing for using while Q is active for extra damage. Note that the cooldown DOES start even before you fire off your second shot, so there is no real need to just pop off the second one to start the cooldown.=
The Equalizer (Ultimate): Rumble calls down a line of rockets over the target location. Enemies in the scorched area take damage over time and are slowed.
=Such a beast of a move. It takes a lot of practice to use this to its maximum benefit, and even more so to do so quickly enough. I like to start a gank with this move, or use it when they are running in a straight line to get away from me so I can trap them in my Q. The DoT effect of this is also pretty killer.=
Exhaust and Ignite are the summoner spells of choice, slowing them down inside your Q and hitting them with Ignite while slapping them with E for extra damage is an easy way to get a kill.
Ghost is another excellent summoner spell, and i've always been a fan of Teleport. Swap out ignite for either of the two if you choose to do so.
So I just recently did 4 matches in a row, here are my results with this build played the way it was intended.
If you have like this build please comment or thumbs up it. I'm tired of so many close minded players giving it a bad rating just because it's different from how they play Rumble.
Overall while I haven't had a TON of time to test out this build, the matches I have played has ended with scores like 21/5/17, and 22/6/16 to point out a couple of my wins. Most of them are similar to those scores.