A solid cube of metal has sides 18 centimeters long. A jeweler melts down the cube and uses all the molten metal to make three smaller cubes of exactly the same size. What is the length in centimeters of an edge of one of these smaller cubes?

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A solid cube of metal has sides 18 centimeters long. A jeweler melts down the cube and uses all the molten metal to make three smaller cubes of exactly the same size. What is the length in centimeters of an edge of one of these smaller cubes?