As a continuation of our recently published work, we have used the pair approximation in Kikuchi version to investigate martensitic and austenitic transformations in homogeneous (HM) and composite (CM) cubic nanoparticles (CNPs) based on the Blume-Emery-Griffiths model. A single cubic nanoparticle made of a core surrounded by a surface is considered as shaped in two dimensional (2D) square arrays instead of hexagonal array. From the phase diagrams of HM and CM-CNPs it has been observed that the martensitic-austenitic transformations (MT-AT) occurred. The influence of the exchange coupling and single-ion anisotropy parameters in the model Hamiltonian on the MT-AT is studied and analyzed in comparison with the results for hexagonal nanoparticles. Significant changes of the phase transition points and hysteresis behaviours depending upon the particle structure have been discussed. (C) 2014 Elsevier B.V. All rights reserved.