Dmitri has a collection of identical cubes. Each cube is labelled with the integers 1 to 6 as shown in the following net: the top row contains 5; the middle row contains, from left to right, 4, 6, 3, 1; the bottom row contains 2. (This net can be folded to make a cube.) He forms a pyramid by stacking layers of the cubes on a table, as shown, with the bottom layer being a 7 by 7 square of cubes. Determine the total number of cubes used to build the pyramid. Explain how you got your answer.
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