Example 4 In the tetrahedron $ABCD$, it is known that
$$
\begin{array}{l}
AB=CD=2 \sqrt{13}, BC=AD=\sqrt{41}, \\
AC=DB=\sqrt{61} .
\end{array}
$$

Then the volume of the tetrahedron is $\qquad$
Notice that,
$$
4^{2}+5^{2}=41,4^{2}+6^{2}=52,5^{2}+6^{2}=61 \text {. }
$$

As shown in Figure 4, the tetrahedron $A B C D$ is extended to the rectangular parallelepiped $A M D N-P C Q B$, where $A N=4, A M=$ $5, A P=6$.

It can be calculated that the volume of the rectangular parallelepiped $A M D N-P C Q B$ is 120.

The volumes of tetrahedrons $P A B C$, $M A C D$, $Q B C D$, and $N A B D$ are all 20, thus