Sweet Building

An army of worker ants was carrying sugar cubes back to their colony. In there, the ants put 1 sugar cube into the first room, 2 into the second, 4 into the third, and doubling the amount so on until the \(101^\text{th}\) room.

Then the Queen ant decided to build bigger cubic blocks of \(5\times 5\times 5\) sugar cubes from all they had previously collected. How many sugar cubes would be remained after all these build-ups?

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