John has yellow, green, and red cubes, each with side length c. Eight yellow cubes are glued together to make a larger cube. An even larger cube is made by gluing on green cubes until no yellow cubes can be seen. After that, John covers the green cubes with red ones so that green also cannot be seen, making an even larger cube. The minimum number of green and red cubes were used to cover previous colors. What is the volume of the final big red cube?
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