Easy does it! The Smart Scholar Method

It is easy to arrive at the answer by working backwards. Try each option and discard if not fine.

The answer would be certainly even. It is easy to see that 2/3 of the answer should be a square and 3/8 of the answer should be a cube. Only 1944 fits.

Sanity check

As the order is for 1944 blocks, half of it, namely, 972 blocks were divided into three sets of 324 each by Tommy and arranged into three 18*18 squares.

During the week, Casper had made 972*3/4 = 729 blocks which Tommy stacks into a 9*9*9 cube.

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