We consider the radiation of three soft gluons in a generic
process for multiparton hard scattering in QCD. In the soft limit
the corresponding scattering amplitude has a singular behaviour that
is factorized and controlled by a colorful soft current. We compute
the tree-level current for triple soft-gluon emission from both
massless and massive hard partons. The three-gluon current is
expressed in terms of maximally non-abelian irreducible
correlations. We compute the soft behaviour of squared amplitudes
and the colour correlations produced by the squared current. The
radiation of one and two soft gluons leads to colour dipole
correlations. Triple soft-gluon radiation produces in addition
colour quadrupole correlations between the hard partons. We examine
the soft and collinear singularities of the squared current in
various energy ordered and angular ordered regions. We discuss some
features of soft radiation to all-loop orders for processes with two
and three hard partons. Considering triple soft-gluon radiation
from three hard partons, colour quadrupole interactions break the
Casimir scaling symmetry between quarks and gluons. We also present
some results on the radiation of four soft gluons from two hard
partons, and we discuss the colour monster contribution and its
relation with the violation (and generalization) of Casimir scaling.
We also compute the first correction of $(1/N_c^2)$ to the eikonal
formula for multiple soft-gluon radiation with strong energy
ordering from two hard gluons.