In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let ${alpha}$ : G${ ightarrow}$ AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product $mathbb{M}=M{ imes}{alpha}$ G of M and G with respect to ${alpha}$ is a von Neumann algebra acting on $H{igotimes}{iota}^2(G)$, generated by M and $(u_g)_g{in}G$, where $u_g$ is the unitary representation of g on ${iota}^2(G)$. We show that $M{ imes}{alpha}(G_1;*;G_2)=(M;{ imes}{alpha};G_1);*_M;(M;{ imes}{alpha};G_2)$. We compute moments and cumulants of operators in $mathbb{M}$. By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if $F_N$ is the free group with N-generators, then the crossed product algebra $L_M(F_n){equiv}M;{ imes}{alpha};F_n$ satisfies that $$L_M(F_n)=L_M(F_{{kappa}1});*_M;L_M(F_{{kappa}2})$$, whenerver $n={kappa}_1+{kappa}_2;for;n,;{kappa}_1,;{kappa}_2{in}mathbb{N}$.