Snapped Bolt

I snapped one of the bolts that holds my water pump into the block and drilled a hole in the broke bolt so i could use an e.z out to get the bolt out. My plan back fired and the e.z out snapped inside the hole i drilled in the bolt, and now i can't drill through the snapped piece of e.z out because my bit won't cut through it. Any advice

Did the bolt break flush with the block? If not, remove the water pump and soak the bolt remains with PB blaster and use BIg vicegrips to remove it.
If it is flush you may well be screwed. The ONLY thing that is going to get that E Z out out of there is to drill it with a CARBIDE bit. Start with a 3/32" carbide bit and STAY centered on the E Z out. Next drill it with a 1/8" carbide or cobalt, then a 5/32", then 3/16" and keep going up in size until you get the E Z out gone. Speaking of which...what size E Z out did you use? If it was a #2 then you used too small of one. You want to use a #3 minimum ( the bolt is 3/8" diameter) and get it in deep so it gets a good solid grip.

A carbide bit will cut through that e.z out then huh. I used a #1, at the time it seemed like if i went any bigger, then the hole i drilled in the bolt would be the same size as the bolt which would be just like drilling it out. I will try the carbide bit though, and a bigger ez out. I appreciate the advice.

You didn't say what type/size engine but the standard SBC uses 3/8" bolts to hold the water pump on.
Since it was a #1 E Z out you may not be able to drill it, too small. The Carbide bit may catch on the edge of the E Z out and break. If you have an air compressor you could start by putting a socket over the bolt with the broken E Z out in it and use an air hammer with a flatened out chisle in it. Hit the socket with it and see if you can rattle the E Z out from the bolt.

If the bolt is broken off flush you may be able to weld a nut to the end. Sometimes the heat of the weld helps loosen the bolt. Good luck.

^^^^ good idea if you heat the bolt enough it should come ot easely