A "Boggle"-ing Problem

In the game "Boggle", the standard game board consists of 16 cubes, each with 6 distinct letters on them. The player shakes the board to create a unique game board for each round. If shakes are totally uninfluenced and random, how many different possible game boards are there? (Disregard rotations of boards when calculating.)

Not intended to violate the copyright of Hasbro IncĀ©.

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