2001 AIME II Problem 15

Let EFGH, EFDC, and EHBC be three adjacent square faces of a cube, for which EC = 8, and let A be the eighth vertex of the cube. Let I, J, and K, be the points on \overline{EF}, \overline{EH}, and \overline{EC}, respectively, so that EI = EJ = EK = 2. A solid S is obtained by drilling a tunnel through the cube. The sides of the tunnel are planes parallel to \overline{AE}, and containing the edges, \overline{IJ}, \overline{JK}, and \overline{KI}. The surface area of S, including the walls of the tunnel, is m + n\sqrt {p}, where m, n, and p are positive integers and p is not divisible by the square of any prime. Find m + n + p.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.