Let r and s be positive integers. Derive a formula for the number of ordered quadruples $(a, b, c, d)$ of positive integers such that
$$3^{r}·7^{s}=
\mathrm{lcm}[a,b,c]=\mathrm{lcm}[a,b,d]=\mathrm{lcm}[a,c,d]=\mathrm{lcm}[b,c,d]$$.
Please provide the value of the formula when r = 2 and s = 1. The answer should be the sum of the coefficients of the expanded expression of the original answer.

Let's think step by step and output the final answer within \boxed{}.
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