For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,;k)=sumlimits_{j=1}^k((frac{j}{k}))((frac{hj}{k})),$$ where $$((x))={{x-[x]-frac{1}{2},;if;x;is;not;an;integer; atop ;0,;;;;;;;;;;if;x;is;an;integer.}$$ J. B. Conrey et al proved that $$sumlimits_{{h=1}atop {(h,k)=1}}^k;s^{2m}(h,;k)=fm(k);(frac{k}{12})^{2m}+O((k^{frac{9}{5}}+k^{{2m-1}+frac{1}{m+1}});log^3k).$$ For $m;{geq};2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$sumlimits_{{h=1}atop {(h,k)=1}}^k;s^2(h,;k)=frac{5}{144}k{phi}(k)prod_{p^{alpha}{parallel}k}[frac{(1+frac{1}{p})^2-frac{1}{p^{3alpha+1}}}{1+frac{1}{p}+frac{1}{p^2}}];+;O(k;{exp};(frac{4{log}k}{loglog{k}})).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.