  We report results of a systematic numerical analysis of interactions between
three-dimensional (3D) fundamental solitons, performed in the framework of the
nonlinear Schr\"{o}dinger equation (NLSE) with the cubic-quintic (CQ)
nonlinearity, combining the self-focusing and defocusing terms. The 3D NLSE
with the CQ terms may be realized in terms of spatiotemporal propagation of
light in nonlinear optical media, and in Bose-Einstein condensates, provided
that losses may be neglected. The first part of the work addresses interactions
between identical fundamental solitons, with phase shift $% \varphi $ between
them, separated by a finite distance in the free space. The outcome strongly
changes with the variation of $\varphi $: in-phase solitons with $\varphi =0$,
or with sufficiently small $\varphi $, merge into a single fundamental soliton,
with weak residual oscillations in it (in contrast to the merger into a
strongly oscillating breather, which is exhibited by the 1D version of the same
setting), while the choice of $% \varphi =\pi $ leads to fast separation
between mutually repelling solitons. At intermediate values of $\varphi $, such
as $\varphi =\pi /2$, the interaction is repulsive too, breaking the symmetry
between the initially identical fundamental solitons, there appearing two
solitons with different total energies (norms). The symmetry-breaking effect is
qualitatively explained, similar to how it was done previously for 1D solitons.
In the second part of the work, a pair of fundamental solitons trapped in a 2D
potential is considered. It is demonstrated that they may form a slowly
rotating robust \textquotedblleft molecule", if aninitial kicks are applied to
them in opposite directions, perpendicular to the line connecting their
centers.
