Post-hoc explanation depends on how model queries are organized. We propose CUBE, a design-based framework that explains a trained predictive model through balanced low--high probes. Selected variables define factors, designed feature-level combinations define query conditions, and model predictions are summarized as factorial contrasts. CUBE reports main effects and pairwise interactions as controlled readings of average and conditional response changes over a declared design space. Experiments on synthetic and real tabular tasks show that CUBE recovers dominant learned effect structure, clarifies query-efficient identifiability, and supports screening--follow-up refinement.