Structures and energetics of B2Li6 are predicted at HF, MP2 and B3LYP/6-31G(d) including energy evaluations at G2MP2, CBS-Q, and B3LYP/6-311G(2d). Six minima are identified on the singlet surface. The cohesive (B2Li6 --> B-2 + Li-6) and Li-2 elimination energies indicate significant stability for the global minimum 3a, which is a B-2 unit with two bridging Li ligands and a bridging tetrahedral Li-4 unit. Sandwich structure 3d, containing two triangular Li-3 units and relating to a C2Li6 isomer is 6.9 kcal/mol less stable. Diborane[6]-like structure 3g is not a minimum.