We design a 3D acoustic metamaterial having a coiling resonant structure with high symmetry. Eigenstate analysis reveals that such a 3D metamaterial has two significant Mie-type eigenmodes, monopole and dipolar resonances. Large blocking of sound waves in the low-frequency range between monopole and dipolar resonances is observed numerically and experimentally. The effective properties extracted from the reflection and transmission coefficients show negative bulk modulus around the monopole resonant frequency and negative mass density around the dipolar resonant frequency. By employing the proposed two-scale model, the metamaterial system demonstrates the functionalities of sound cloaking and super-tunneling within a finite space.

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