6 Answers

I don't know, but I think my mom was worried I would grow them in my ears as a kid! 

Well, if you have proper lighting used to grow plants "grow lights" & a very large pot of soil that can drain you can try it.  One potato can yield a whole bunch of them which is why you need a large container

Potatoes are root vegetables, are they not?  You would need a fairly deep bed. The cost of providing the light and temp you need might not be worth the price of a  sack of potatoes.  

Why not grow mushrooms, they don't need light?

It is possible with the help of LED grow light kits. These will help your potatoes to survive even without light coming from the sun. Just visit http://growblu.com/ for more details.