Catalyzes the conversion of (2E,6E)-farnesyl diphosphate (FPP) to yield the bicyclic sesquiterpenol 4-epi-cubebol via a 1,10-cyclization, which requires the abstraction of the pyrophosphate from FPP to yield a (E,E)-germacradienyl cation (PubMed:27666571, PubMed:27829890). The only accepted substrate is (2E,6E)-farnesyl diphosphate (FPP) (PubMed:27829890). (2E,6E)-farnesyl diphosphate + H2O = 4-epi-cubebol + diphosphate Binds 3 Mg(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Xaa-Glu (DDXXXE) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.