  In this paper, we give the explicit structure of $ \otimes^{3} H $ and $
\wedge^{3} H $ where $ H $ is a generalized Heisenberg Lie algebra of rank at
most $ 2. $ Moreover, for a non-abelian nilpotent Lie algebra $ L, $ we obtain
an upper bound for the dimension of $ \otimes^{3} L.
