Let f and g be two distinct normalized primitive holomorphic cusp forms of even integral weights \(k_{1}\) and \(k_{2}\) for the full modular group \(\Gamma =SL(2,\mathbb {Z})\) , respectively. Let \(\lambda _{f\times f\times g}(n)\) be the nth coefficient of the Dirichlet expansion of the triple product L-function \(L(f\times f\times g,s)\) . In this paper, we investigate the asymptotics for the average behaviour of the second and fourth power moments of \(\lambda _{f\times f\times g}(n)\) on the sequence of positive integers represented by primitive integral positive definite binary quadratic forms of a given discriminant D. By analogy, we also obtain similar results for the average behaviour of fourth power moment of the coefficients \(\lambda _{\text {sym}^{2}f\times f}(n)\) of Rankin-Selberg L-function \(L(\text {sym}^{2}f\times f,s)\) .
