Example 8. Calculate $(\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}$
$$
\begin{array}{l}
+\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7}) \\
\cdot(-\sqrt{5}+\sqrt{6}+\sqrt{7}) .
\end{array}
$$
Analyze the repeated application of the difference of squares formula to get the result as 104.