Cubic Doublers

Normal sudoku rules apply.

Digits in cages do not repeat, and must sum to a perfect cube (i.e. cage totals are 1, 8, or 27).

The grid contains 9 doublers, one in each row, column, and box. For purposes of cage totals, cells on doublers count as double their value. Each digit from 1 through 9 is doubled exactly once.