  We present a theoretical method to determine the multipartite entanglement
between different partitions of multimode, fully or partially symmetric
Gaussian states of continuous variable systems. For such states, we determine
the exact expression of the logarithmic negativity and show that it coincides
with that of equivalent two--mode Gaussian states. Exploiting this reduction,
we demonstrate the scaling of the multipartite entanglement with the number of
modes and its reliable experimental estimate by direct measurements of the
global and local purities.
