Prototyping large, electronically integrated structures is challenging and often results in unwieldy wiring, weak mechanical properties, expensive iterations, or limited reusability. While many electronics prototyping kits exist for small-scale objects, relatively few methods exist to freely iterate large and sturdy structures with integrated electronics. To address this gap, we present the Voxel Invention Kit (VIK), which uses reconfigurable blocks that assemble into high-stiffness, lightweight structures with integrated electronics. We do this by creating cubic blocks composed of PCBs that carry electrical routing and components and can be (re)configured with simple tools into a variety of structures. To ensure structural stability without expertise, we created a tool to configure structures and simulate applied loads, which we validated with mechanical testing data. Using VIK, we produced devices reconfigured from a shared set of voxels: multiple iterations of a customizable AV lounge seat, a dance floor game, and a force-sensing bridge.