Recent proliferation of mobile devices and edge servers (e.g., small base stations) strongly motivates distributed learning at the wireless edge. In this paper, we propose a fast and secure distributed learning framework that utilizes computing resources at edge servers as well as distributed computing devices in tiered wireless edge networks. Our key ideas are to utilize 1) two-tier computing (leveraging computing powers of both ESs and devices), 2) hierarchical coding (allowing redundant computation at the nodes to combat Byzantine attacks at both tiers) and 3) broadcast nature of wireless devices (located in the overlapping cell region). A fundamental lower bound is first derived on the computational load that perfectly tolerates Byzantine attacks at both tiers. Then we propose TiBroco, a hierarchical coding framework achieving this theoretically minimum computational load. Experimental results show that TiBroco enables fast and secure distributed learning in practical tiered wireless edge networks plagued by Byzantine adversaries.