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cubic n.  and  untouchable n.

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(max 15 digits)

First numbers that belong to both sets:

216, 1728, 5832, 8000, 13824, 21952, 27000, 74088, 110592, 157464, 175616, 195112, 216000, 238328, 287496, 314432, 343000, 373248, 729000, 884736, 941192.