Mobile microrobots are envisioned to be useful in a wide range of high-impact applications, many of which requiring cohesive group formation to maintain self-bounded swarms in the absence of confining boundaries. Cohesive group formation relies on a balance between attractive and repulsive interactions between agents. We found that a balance of magnetic dipolar attraction and multipolar repulsion between self-assembled particle chain microrobots enable their self-organization into cohesive clusters. Self-organized microrobotic clusters translate above a solid substrate via a hydrodynamic self-propulsion mechanism. Cluster velocity increases with cluster size, resulting from collective hydrodynamic effects. Clustering is promoted by the strength of cohesive interactions and hindered by heterogeneities of individual microrobots. Scalability of cohesive interactions allows formation of larger groups, whose internal spatiotemporal organization undergoes a transition from solid-like ordering to liquid-like behavior with increasing cluster size. Our work elucidates the dynamics of clustering under cohesive interactions, and presents an approach for addressing operation of microrobots as localized teams.