Suggestion: Let $a=\sqrt{2 n+1}$ and $b=$ $\sqrt{2 n-1}$.

Facts that Help: Use the identity

$\left(a^{2}+a b+b^{2}\right)(a-b)=a^{3}-b^{3}$.
For a positive integer $n$ consider the function

$$
f(n)=\frac{4 n+\sqrt{4 n^{2}-1}}{\sqrt{2 n+1}+\sqrt{2 n-1}}
$$

Calculate the value of

$$
f(1)+f(2)+f(3)+\cdots+f(40)
$$