Is that the only bit of the stud that is accessible? Drilling it out will not be easy due to the casting being soft.
Can you (or a helpful friend) place a nut about the same size on the broken stud and weld inside through to the broken stud? The heat from the weld will help crack the corrosion in the thread. Wait for it to cool for a short while before having a wiggle at it. Once it's out, you can check the thread.
You might struggle to remove the stud otherwise, the thread will probably be corroded due to dissimilar metals.
Failing that, a trip to the scrappers is in order.