Distributed source seeking in a three-dimensional (3-D) environment without explicit estimation of the gradient of the field is challenging. Nevertheless, for a swarm of an arbitrary number of agents, we develop a strategy to perform a source seeking behavior by requiring agents to synchronize their direction of motion using only local interactions while modulating their speed based only on the field value measured by each agent. The agents collectively move toward the source without estimating gradient and without sharing measurements of the field. We formulate a cascaded input-to-state stability problem from which we obtain Lyapunov-based convergence and robustness results. We validate the convergence of the swarm to the minimum of the field through simulated source seeking behavior in a 3-D scalar field.