In this paper, we consider several convolution sums, namely, $A_i(m,n;N)$ ($i=1,2,3,4$ ), $B_j(m,n;N)$ ($j=1,2,3$ ), and $C_k(m,n;N)$ ($k=1,2,3,？,12$ ), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity involving the Weierstrass $\wp$ -function, its derivative and certain linear combination of Eisenstein series is established.