Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL(2, Z), and let λ f (n), σ(n) and φ(n) be the nth normalized Fourier coefficient of the cusp form f , the sum-of-divisors function and the Euler totient function, respectively. In this paper, we investigate the asymptotic behaviour of the following summatory function S j,b,c (x) := n=a 2 1 +a 2 2 +a 2 3 +a 2 4 ≤x (a 1 ,a 2 ,a 3 ,a 4)∈Z 4 λ j f (n)σ b (n)φ c (n), where j ≥ 2 is any given integer. In a similar manner, we also establish other similar results related to normalized coefficients of the symmetric power L-functions associated to holomorphic cusp form f .