9. Arrange the positive integers (excluding 0) that are neither perfect squares nor perfect cubes in ascending order, resulting in 2, $3,5,6,7,10, \cdots \cdots$, what is the 1000th number in this sequence?
【Analysis】From 1 to 1000, there are $1^{2}$ to $31^{2}$, a total of 31 square numbers, and $1^{3}$ to $10^{3}$, a total of 10 cube numbers. Numbers that are both square and cube numbers are $1^{6}$ to $3^{6}$, a total of 3. Therefore, from 1 to 1000, $31+10-3=38$ numbers will be removed. From 1001 to 1038, there is $32^{2}$, a total of 1 square number, and no cube numbers, so one number will be removed. Therefore, the 1000th number in the original sequence is 1039.