It is well-known that the classical Dedekind sums \(S(h,k)\) first arose in the transformation formula of the logarithm of the Dedekind-eta function. If \(h\) and \(k\) are coprime integers with \(k>0\), the Dedekind sum is defined by \[ S(h,k)=\sum\limits_{\mu\mod k}((\frac{\mu}{k}))((\frac{h\mu}{k})), \] where \(((x))\) is defined by \[ ((x))=\begin{cases} x-[x]_{G}-\frac{1}{2}, & x\text{ is not an integer} \\ 0, & \text{otherwise} \end{cases} \] where \([x]_{G}\) is the largest integer \(\leq x\). Generalized Dedekind sums \(S_{p}(h,k)\) are defined as follows: \[ S_{p}(h,k)=\sum_{a\text{mod}k}\frac{a}{k}\overline{B}_{p}(\frac{ah}{k}), \] where \(h\) and \(k\) are coprime positive integers and \(\overline{B}_{p}(x)\) is the \(p\)-th Bernoulli function, which is defined as follows: \[ \begin{aligned} \overline{B}_{p}(x) & =B_{p}(x-[x]_{G}) \\ & =-p!\left( 2\pi i\right) ^{-p}\sum_{\substack{{m=-\infty}\\ {m\not =0}}}{}^{\infty}m^{-p}e^{2\pi imx}, \end{aligned} \] where \(B_{n}(x)\) is the usual Bernoulli polynomials. Observe that when \(p=1\), the sums \(S_{1}(h,k)\) are known as the classical Dedekind sums, \(S(h,k)\). In this paper, the authors have given mean values of \(L\)-functions, Dedekind sums and also Dedekind-Rademacher sums. The authors prove a \textit{reciprocity law} of these sums. Their results improve previous works of \textit{H. Walum} [Ill. J. Math. 26, 1--3 (1982; Zbl 0464.10030)], \textit{S. R. Louboutin} [Publ. Math. 78, No. 3--4, 647--658 (2011; Zbl 1240.11133)], and \textit{H. Liu} and \textit{W. Zhang} [Acta Arith. 122, No. 1, 51--56 (2006; Zbl 1108.11062)].