64 125 216 343 512 729
Bold numbers are the missing in the sequence
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343.
1 8 27 64 125 216 343
2 cubed is 8.3 cubed is 27.4 cubed is 64.5 cubed is 125.6 cubed = 216.7 cubed is 343.
-5,-2,1,4,7**
The sequence appears to be alternating between cubes of integers and their negative counterparts. The first number is -4 cubed, the second is 5 cubed, the third is -6 cubed, the fourth is 7 cubed, and the fifth is -8 cubed. Therefore, the next number in the sequence would be 8 cubed, which is 512.