Edit: Thanks Wrench, you beat me to it.
Putting that much force on a 5/16" cable will snap it, no question.
One thing to keep in mind is that when doing a double line pull, it is the block that is taking the load.
so using the 8,000 lb Warren winch on a single line pull the max pull will be 8,000 pounds. if you run a double line (0 degree pull) on a single block you divide the load on the cable but the full pull weight will be seen at the block. so in this case on a 0 degree pull your (2 to 1 advantage) 8,000 pound winch can now generate a total of 16,000 pounds. Each half of the cable will still only see 8,000 Lbs. now here is the key, and why I mentioned that your blocks need to handle it, the block will see the FULL 16,000 Lbs of pull. your choke chain/tree saver snatch block and associated hardware MUST be able to handle the load. Remember, this is in a moving block configuration.
I agree with 38377k5, you are most likely going to need to move to the front as your rear attach point is no longer viable. Also, as he mentioned getting the truck further out of the mud first will help tremendously.
Think of it this way. The charts for calculating pull stuck to the rim is a 1x multiplier. Stuck to the wheel (think wheel hub) is a 2x multiplier. stuck to the body/frame is a 3x multiplier. Every inch you clear out of that mud makes a BIG difference.
Rufus