  It is well known that a particle cannot freely share entanglement with two or
more particles. This restriction is generally called monogamy. However the
formal quantification of such restriction is only known for some measures of
entanglement and for two-level systems. The first and broadly known monogamy
relation was established by Coffman, Kundu, and Wootters for the square of the
concurrence. Since then, it is usually said that the entanglement of formation
is not monogamous, as it does not obey the same relation. We show here that
despite that, the entanglement of formation cannot be freely shared and
therefore should be said to be monogamous. Furthermore, the square of the
entanglement of formation does obey the same relation of the squared
concurrence, a fact recently noted for three particles and extended here for N
particles. Therefore the entanglement of formation is as monogamous as the
concurrence. We also numerically study how the entanglement is distributed in
pure states of three qubits and the relation between the sum of the bipartite
entanglement and the classical correlation.
