Terpene cyclase that catalyzes the cyclization of farnesyl diphosphate (FPP) to various sesquiterpenes, including beta-elemene gamma-cadinene, delta-cadinene, and alpha-cadinene. (2E,6E)-farnesyl diphosphate = delta-cadinene + diphosphate The conserved DDXXD and NSE/DTE motifs are important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.