Summary: Let \(\widetilde{M}\) be a complex manifold, \(\Gamma\) be a torsion-free cocompact lattice of \(\mathrm{Aut}(\widetilde{M})\) and \(\rho :\Gamma \rightarrow SU(N,1)\) be a representation. Suppose that there exists a \(\rho\)-equivariant totally geodesic isometric holomorphic embedding \(\imath :\widetilde{M}\rightarrow\mathbb{B}^N\). Let \(M:=\widetilde{M}/\Gamma\) and \(\Sigma :=\mathbb{B}^N /\rho (\Gamma)\). In this paper, we investigate a relation between weighted \(L^2\) holomorphic functions on the fiber bundle \(\Omega :=M\times_{\rho} \mathbb{B}^N\) and the holomorphic sections of the pull-back bundle \(\imath^* (S^m T^*_{\Sigma})\) over \(M\). In particular, \(A^2_{\alpha} (\Omega)\) has infinite dimension for any \(\alpha >-1\) and if \(n<N\), then \(A^2_{-1}(\Omega)\) also has the same property. As an application, if \(\Gamma\) is a torsion-free cocompact lattice in \(SU (n, 1), n\geq 2\), and \(\rho :\Gamma \rightarrow SU(N,1)\) is a maximal representation, then for any \(\alpha >-1, A^2_{\alpha} (\mathbb{B}^n \times_{\rho} \mathbb{B}^N)\) has infinite dimension. If \(n<N\), then \(A_{-1}^2 (\mathbb{B}^n \times_{\rho} \mathbb{B}^N)\) also has the same property.