A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side. If the length and width of the base are doubled, how many cubes could the new box hold?

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A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side. If the length and width of the base are doubled, how many cubes could the new box hold?

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