Front cylinder dumping raw fuel, exits under exhaust pipe. Cylinder not firing.

Ordinarily, rough running with a raw gas smell indicates a fuel pressure regulator or fuel injector problem, but that usually produces grey or black smoke. The white smoke may be steam, which is more serious.

If the exhaust also smells somewhat like maple syrup (that's what burned engine coolant smells like unless you are running water without antifreeze), or your coolant level is going down rapidly, you probably have a bad head gasket, cracked block or head that is leaking coolant into one or more cylinders. That's what would produce a large amount of steam, and the uneven power production is what makes the engine vibrate strongly. The mixture control system is being all messed up because the coolant in the cylinder is preventing proper combustion - on the one hand the knock vibration sensor is telling the computer that the engine is running too lean, but on the other hand the oxygen sensor is detecting the rich condition. A readout of the engine computer would be interesting to see.

Run the engine as little as possible until you get this checked out. A coolant leak into a cylinder can cause quite a bit of secondary damage.

You may be able to identify which cylinder has the problem by removing the spark plugs and inspecting them. A wet spark plug is confirmation of my hypothesis. If you have a borescope (video camera on a flexible tube or with a fiber optic bundle with a lens on the end), you can peek inside the cylinder through the spark plug hole. Otherwise, pull the head to see where the coolant leak is.

possibly but indicates a problem injector , leaking or faulty seals causing a flooding condition in that cylinder

If you have raw fuel coming out of the exhaust pipe , you have real issues. There are a couple reasons this can happen.

1. You have a dead cylinder and the fuel is not being burned and is exhausted thru the tailpipe. This is unusual since most of the time if this occurs during operation the catalytic converter is hot enough to burn off the excess fuel.

2. You have a frozen injector and it is leaking into the cylinder after shutdown. Hard to believe this though, as you'd need a good bit of fuel to fill a cylinder to where it could flow out through an open exhaust valve. Usually the fuel would wash down past the piston rings first into the oil pan.

Hi Mark:
My train of thought is along the line that for unburned fuel to get into the exhaust manifold, it still has to go through a cylinder so there is either no spark to light it up, or it's so rich that it's not burning. Have you had a chance to check the plug tips for indicators as to what's happening in the combustion chamber?
Just an Old Dude thinking out loud and typing it down...

If cylinder 2 is not firing first check for good compression on that cylinder. If compression is good try swapping coils from say #3 and the #2 cylinders. If #3 now don't fire and #2 does it is a bad coil. If it don't change then chances are the injector is bad. You can also swap injectors the same way.

If this is still under the Warranty, back to the Dealer it goes. If you had to pay for an unneeded part, ask for compensation.
The sparkplug and coil get a signal to fire from the PCM. If the signal is not getting to the #8 coil/plug, then you need to move upstream to the PCM. Something may be corroded in the connector for that single cylinder.
The other test is the Noid test for injector firing. You might want to throw a new injector into the #8 spot and see if it helps.
Finally, the rear cylinders,4 and 8, have been used to route exhaust gas to the EGR. This is an additional duty that may effect exhaust flow on that single cylinder.
You did not state the year of your vehicle. For a time, a part called a "Cam Phaser" on 4.6L and 5.4L V-8 engines would cause timing issues inside the motor. Each side of the motor is independently timed, so you can have an issue on only one side of the motor. Perhaps with cylinder 8, a combination of events is causing your problem and when both the EGR flow demands from cylinder 8 and improper timing from a bad "Cam Phaser" causes a misfire. The "Lean Code" which has not appeared is an average of all 4 cylinders on one bank. Since you are not dumping "Raw, unburned fuel" from cylinder 8, we can assume that cylinder 8 is running lean and may not even be getting fuel.

P0305 code is a cylinder #5 missfire. The codes last digit is the effected cylinder, i.e. P0305 is cylinder #5 and a P0302 is cylinder #2 and so on. A P0300 is a multi-cylinder missfire.
Thoery 1: Ignition system! If the cylinder is being injected with fuel and not getting spark, the un-burned fuel would simply be pumped out the exhaust system and can be the source of the fuel smell. Check the ignition system and the firing order. I know you said you already did this, but I have to include this for other people in the future who might be using this to help them with a simillar problem.
Theory 2: Bad injector! If #5 cylinder injector is stuck at full fuel (leaking badly due to an internal mechanical failure) it will be pumping way too much fuel into the cylinder for the cylinder to burn. The outcome is the same as before, it just pumps the raw fuel out the exhaust system. Just as before, compare 2 cylinders by inspecting the spark plugs of #3 and #5. If an injector is stuck, that cylinder spark plug will be soaked with fuel. Injectors cannot be repaired, just replaced.
Theory 3: Low compression! If #5 cylinder is low on compression it will not fire the fuel as it is injected. A simple compression test is needed to tell if there is a mechanical failure internal to the engine causing low compression.
Theory 4: Bad intake plenum gasket! The intake manifold has a steel plate bolted onto the bottom of it with a gasket called a plenum. This plate is inside the lifter valley. If this gasket fails it will cause a vaccume leak into the intake manifold that will create a lean mixture condition for the cylinder that is nearest the failed spot. This lean mixture does not light or burn effectivly and can cause an unburned mixture to enter exhaust manifold causing the same sympoms as above.
Obviously this problem needs further diagnostics to pin-point the source of the failure. These are simply starting points and there can be many other things that can cause this type of problem, but these are the most likely. Hope this can be of some help, have more questions? Just ask!

white smoke usually means that your car is dumping raw fuel into the cylinder without burning off. You may have a bad injector or fuel pressure regulator.

injector assembly under upper plenum is broken. r and r upper plenum and replace injector assembly.

IF YOU GOT CYLINDER MISFIRE.OR OPEN FUEL INJECTOR.THAT WILL CAUSE THE PCM TO ENRICHEN FUEL MIXTURE.TO ADJUST TO DEAD CYLINDER.WHICH ACT AS A LARGE VACUUM LEAK.THATS WHY YOUR EXHAUST TAIL PIPES HAS A RAW FUEL SMELL AND WHITE SMOKES.