961
【Solution】According to the analysis, the largest "Hope Number" within 1000 is the largest perfect square within 1000,

and it is known that the largest perfect square within 1000 is $31^{2}=961$,
According to the divisor sum theorem, the number of divisors of 961 is: $2+1=3$ (divisors), which meets the requirement,
Answer: The largest Hope Number within 1000 is 961.
Therefore, the answer is: 961.
8. (6 points) If a natural number has an odd number of divisors, we call this natural number a "Hope Number". Then, the largest "Hope Number" within 1000 is

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