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alternating n.  and  cubic n.

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(max 15 digits)

First numbers that belong to both sets:

1, 8, 27, 125, 216, 343, 729, 5832, 12167, 614125, 658503, 1030301, 1092727, 4741632, 8741816, 27270901, 27818127, 47832147, 381078125.