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For Geeks & Brainiacs #09- Tightly Packed -

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Puzzle Image There are three gift boxes: a small cube-shaped box, a sphere-shaped box, and a large cube-shaped box. The small cube-shaped box has a volume of 3,375 cm³. If the small cube-shaped box is placed inside the sphere-shaped box, it's a perfect fit. And if the sphere-shaped box is placed inside the large cube-shaped box, it's also a perfect fit.

Ignoring the thickness of the walls of the boxes, can you find the volume of the large cube-shaped box?
Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?