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.
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343.
1 8 27 64 125 216 343
216
27= 3364=43125=53so next number will be 63 = 216
In the list of cubes, the next number is 216.