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Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then
By substitution, we have that
and 
.
Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>
By substitution, we have that
Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>