Efficient storage of hydrogen is a bottleneck problem for hydrogen-based energy solutions. We demonstrate the feasibility of trapping a pair of hydrogen molecules in beryllium cluster cages. The systems are constructed by merging two smaller units with single molecules trapped, which are known to be stable in isolation. The resulting (H-2)(2)@Be-n species can have hydrogen cores and beryllium shells of different shapes, and we report the calculated energy barriers for hydrogen exit from the cage. The relative stabilities are related to the molecular structure and charge distributions, and some initially counter-intuitive features are explained. Aspects of the release of hydrogen from such structures, and of possible scaling up to larger extended systems of fused cages, are discussed in terms of hydrogen storage. The predicted capacity could potentially be sufficient for practical usage.