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Commercially available 3-D transmission-line matrix method (TLM) software is employed to analyse a cubical cavity resonator loaded concentrically with a cubical dielectric of dielectric constant 37. For the first time, a useful mode chart for seven degenerate modes of the resonator is generated from the computed results of the resonant frequencies. As an application of the mode chart, a triple-mode bandpass Cheb~yshev filter is designed and fabricated using the resonator operating in TM111 mode. The unexpected asymmetry and the transmission zero in the response of the filter are attributed to the coupling between the input and output. When the coupling is characterised, close agreement between the simulated and measured performance of the filter is obtained.