In this paper we present PeerCube, a DHT-based system that aims at minimizing performance penalties caused by high churn while preventing malicious peers from subverting the system through collusion. This is achieved by i) applying a clustering strategy to support quorum-based operations; ii) using a randomised insertion algorithm to reduce the probability with which colluding Byzantine peers corrupt clusters, and; iii) leveraging on the properties of PeerCube's hypercube structure to allow operations to be successfully handled despite the corruption of some clusters. Despite a powerful adversary that can inspect the whole system and issue malicious join requests as often as it wishes, PeerCube guarantees robust operations in O(logN) messages, with N the number of peers in the system. Extended simulations validate PeerCube robustness.