HowmanySquaredivisors

Let the number given be $N$ . Then

$\begin{aligned} N & = 8^6 \times 9^{20} \times 10^{18} \\ & = 2^{3\times 6} \times 9^{20} \times 2^{18} \times 5^{18} \\ & = 2^{36} \times 9^{20} \times 5^{18} \\ & = 4^{\red{18}} \times 9^{\red{20}} \times 25^{\red 9} \end{aligned}$

The number of square divisors of $N$ is $(\red{18}+1)(\red{20}+1)(\red 9+1) = \boxed{3990}$ .