The kidney stone issue aside, I will first say that it is not advisable to drink as many caffeinated energy drinks as you are per day. This much caffeine and other stimulants will raise your blood pressure and could irritate your heart. I would suggest that you start weaning yourself off of the energy drinks and find ways to reduce the amount of caffeine you need. Perhaps you need more sleep at night?
Now on the kidney stone issue. A kidney stone is a hard crystallized object that forms in the kidney and needs to travel out of the body through the urinary system. They are quite common and can be very painful to pass. Drinking caffeinated beverages per se won't increase your chances of getting a stone. I can't speak to the energy drinks you are taking because I don't know their contents. If they contain high amounts of phosphate or calcium then they may increase your chances of getting a stone. While studies addressing this issue are limited, most likely, drinking caffeinated beverages such as coffee will likely decrease kidney stones
rather than cause them.
I suggest that you bring this issue up with your primary care physician
. The two of you can discuss ways you can prevent kidney stones (if you are worried about it) and how to reduce the amount of energy drink you are consuming.