【Solution】Solution: According to the analysis, in the range $2000 \sim 2020$, exclude odd numbers, and from the remaining even numbers, exclude those that cannot be divided by 3,

Finally, only the following numbers remain: 2004, 2010, 2016. Decomposing these numbers into prime factors, we get:
$$
2004=2 \times 2 \times 3 \times 167 ; 2010=2 \times 3 \times 5 \times 67 ; \quad 2016=2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7,
$$

Clearly, the prime factors of 2014 and 2010 do not amount to 7 or more within 1 to 9, which does not meet the requirements, so they are excluded. The only number that meets the requirements is 2016, and the factors of 2016 are: $2, 3, 4, 6, 7, 8, 9$.

Therefore, the answer is: 2016.
7. (10 points) For a natural number $N$, if at least seven of the nine natural numbers from $1-9$ are factors of $N$, then $N$ is called a "Seven-Star Number". Among the natural numbers greater than 2000, the smallest "Seven-Star Number" is $\qquad$