  We calculate the entanglement entropy of blocks of size x embedded in a
larger system of size L, by means of a combination of analytical and numerical
techniques. The complete entanglement entropy in this case is a sum of three
terms. One is a universal x and L-dependent term, first predicted by Calabrese
and Cardy, the second is a nonuniversal term arising from the thermodynamic
limit, and the third is a finite size correction. We give an explicit
expression for the second, nonuniversal, term for the one-dimensional Hubbard
model, and numerically assess the importance of all three contributions by
comparing to the entropy obtained from fully numerical diagonalization of the
many-body Hamiltonian. We find that finite-size corrections are very small. The
universal Calabrese-Cardy term is equally small for small blocks, but becomes
larger for x>1. In all investigated situations, however, the by far dominating
contribution is the nonuniversal term steming from the thermodynamic limit.
