How to prove the outer measure of a compact set in Rn is the infimum of sums of volumes of closed cubes?

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How to prove the outer measure of a compact set in Rn is the infimum of sums of volumes of a finite number of closed cubes? We defined outer measure using an infinite number of cubes, but I don't know why the outer measure of a compact set can be defined using a finite number of cubes....