  The main objective of this work is to investigate the integrability and
linearizability problems around a singular point at the origin of the family of
differential systems Particularly we are interested in the three-dimensional
cubic Lotka-Volterra systems for (1:-1:1) resonant. We give a complete set of
necessary conditions for both integrability and linearizability problems. The
local existences of two independent first integrals guarantee that these
conditions are sufficient as well. Furthermore, we use the Darboux method of
integrability and some other techniques to show that the system admits two
independent first integrals at the origin.
