seven
1 1 = 1 × 1 × 1
2 8 = 2 × 2 × 2
3 27 = 3 × 3 × 3
4 64 = 4 × 4 × 4
5 125 = 5 × 5 × 5
6 216 = 6 × 6 × 6
7 343 = 7 × 7 × 7
assuming 1 cubed counts
as if between 1 and 500 then 1 itself does not count;
so answer then is six.
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43 = 64 53 = 125 63 = 216 73 = 343
496.
They are: 529 and 576
500
400 of them.