In this Letter, we theoretically propose and experimentally demonstrate a three-dimensional soundproof acoustic cage structure, hereby denoted as an acoustic metacage. The metacage is composed of six acoustic metamaterial slabs with open holes and hidden bypass space coiling tunnels connected to the holes. Band structure analysis reveals a novel physical mechanism to open a low-frequency broad partial band gap via the band folding in other directions, which can also be interpreted by an effective medium with indefinite effective mass density and negative effective modulus. Transmission loss in simulations and in the acoustic impedance tube are administered. Strikingly, we prove that the soundproofing effect of the metacage is robust against the airflow perturbation induced by a fan. Our work paves a road for low-frequency airborne soundproof structures in the presence of ventilation.