Close to charge neutrality, the low-energy properties of high-quality suspended devices based on atomically thin graphene layers are determined by electron–electron interactions. Bernal-stacked layers, in particular, have shown a remarkable even–odd effect with mono- and tri-layers remaining gapless conductors, and bi- and tetra-layers becoming gapped insulators. These observations—at odds with the established notion that (Bernal) trilayers and thicker multilayers are semi-metals—have resulted in the proposal of a physical scenario leading to a surprising prediction, namely that even-layered graphene multilayers remain insulating irrespective of their thickness. Here, we present data from two devices that conform ideally to this hypothesis, exhibiting the behavior expected for Bernal-stacked hexa- and octa-layer graphene. Despite their large thickness, these multilayers are insulating for carrier density |n| < 2–3 × 10^10 cm−2, possess an energy gap of approximately 1.5 meV at charge neutrality—in virtually perfect agreement with what is observed in bi- and tetra-layer graphene—and exhibit the expected integer quantum Hall effect. These findings indicate the soundness of our basic insights on the effect of electron interactions in Bernal graphene multilayers, show that graphene multilayers exhibit unusual and interesting physics that remains to be understood, and pose ever more pressing questions as to the microscopic mechanisms behind the semimetallic behavior of bulk graphite.