We have measured ReBCO coated conductor-based CORC® and Roebel cables at 77 K in a Spinning Magnet Calorimeter which subjected the tapes in the samples to a radial magnetic field of 566 mT (peak) at frequencies up to 120 Hz (272 T/s, cyclic average) with an approximately sinusoidal waveform. The samples were oriented such that the field applied to the tapes within the cables was entirely radial, simplifying subsequent analysis. An expression for loss which included hysteretic, flux creep, and eddy current losses was fit to both the CORC® and the Roebel cables. This expression allowed easy comparison of the relative influence of eddy currents and flux creep (or power-law behavior) effects. The loss of both the CORC® and Roebel cables measured here were seen to be essentially the sum of the hysteretic loss, flux creep effects, and the normal metal eddy current losses of the individual tapes. The losses of these cables were measured at high B*dB/dt with no coupling current loss observed under the present preparation conditions. The influence of flux creep effects on loss were not negligible. The losses of the CORC® cable per meter of tape were seen to be reduced from the case of a flat tape because of the helical geometry of the tapes.