Privacy protection is increasingly critical in various applications due to the prevalence of networked systems. In this article, we focus on preserving the privacy of nodes' initial states while computing their average in a network. Curious nodes attempt to identify the initial states of other nodes without interfering in the computation. To address this challenge, we propose two privacy-preserving algorithms. The first algorithm operates over homogeneous networks, i.e., nodes have consistent processing delays and are able to communicate in a synchronous fashion. The second algorithm operates over heterogeneous networks, i.e., nodes have varying processing delays and communicate in an asynchronous fashion. Our algorithms exhibit efficient communication, finite-time convergence, and operation termination after convergence, making them suitable for resource-constrained environments. We also present topological conditions under which our algorithms enable privacy preservation. Finally, we apply our algorithms to a smart grid system and compare their performance against other algorithms, emphasizing their advantages in communication efficiency, convergence rate, and privacy preservation.