Color the surfaces of a cube of dimension $5\times 5\times 5$ red, and then cut the cube into smaller cubes of dimension $1\times 1\times 1$. Take out all the smaller cubes which have at least one red surface and fix a cuboid, keeping the surfaces of the cuboid red. Now what is the maximum possible volume of the cuboid?

Let's think step by step and output the final answer within \boxed{}.
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