We propose polarization-independent and dual-broadband metamaterial absorbers at microwave frequencies. This is a periodic meta-atom array consisting of metal-dielectric-multilayer truncated cones. We demonstrate not only one broadband absorption from the fundamental magnetic resonances but additional broadband absorption in high-frequency range using the third-harmonic resonance, by both simulation and experiment. In simulation, the absorption was over 90% in 3.93-6.05 GHz, and 11.64-14.55 GHz. The corresponding experimental absorption bands over 90% were 3.88-6.08 GHz, 9.95-10.46 GHz and 11.86-13.84 GHz, respectively. The origin of absorption bands was elucidated. Furthermore, it is independent of polarization angle owing to the multilayered circular structures. The design is scalable to smaller size for the infrared and the visible ranges.