I ran into the same problem when I tried baking my god-daughter's "First Communion" cake.
You will need to purchase a heating core for baking cakes that are larger than 9" in diameter. Your local craft store such as Michael's carries the Wilton Heating Core (that is the place I purchased it from and I'm located in Canada). The heating core is set inside the center of the pan before it is filled with batter (lightly greased on both the inside and the outside) and the cake batter is poured around it. A small amount is poured into the cake core itself to create a “plug” for the cake after it has baked. When the cake bakes, some heat radiates outward from the metal core, putting more of the batter closer to a direct heat source and baking a bit faster.
If you are unable to get your hands on a heating core, I have heard cake decorator's using their "Flower Nails". For example, a 12 inch cake would need require three flower nails. Apparently, you coat the nails the same way you coat your pans. Place them together in the middle of the pan. Pour batter in.Bake as normal.
Either one of these methods will solve issue of the inside of the cake being under-cooked white the outside is over-cooked.