Alice is stacking balls on the ground in three layers using two sizes of balls: small and large. All small balls are the same size, as are all large balls. For the first layer, she uses 6 identical large balls A, B, C, D, E, and F all touching the ground and so that D, E, F touch each other, A touches E and F, B touches D and F, and C touches D and E. For the second layer, she uses 3 identical small balls, G, H, and I ; G touches A, E, and F, H touches B, D, and F, and I touches C, D, and E. Obviously, the small balls do not intersect the ground. Finally, for the top layer, she uses one large ball that touches D, E, F, G, H, and I. If the large balls have volume 2015, the sum of the volumes of all the balls in the pyramid can be written in the form a \sqrt{b}+c for integers a, b, c where no integer square larger than 1 divides b. What is a+b+c?