In this work, the influences of biaxial compressive and tensile strains on optical gain and threshold current density are investigated theoretically as a function of the side lengths of the quantum box in the GaN/Al0.2Ga0.8N structure by using a model based on the density matrix theory of semiconductor lasers with relaxation broadening. For various side lengths of the quantum box, we compare the spectra gain curves of compressive, tensile-strained, and unstrained structures of the GaN/Al0.2Ga0.8N cubic quantum-dot (QD) laser. The dependence of peak optical gain on carrier density and the modal gain on current density is plotted too for all cases. The results reveal that many enhancements can be made to the laser structure by introducing -0.5% compressive strain: a higher value of optical gain of 18421 cm-1  at  L=60A, a lower value of transparency of carrier density of Ntr=0.13*10¨¨19 cm-3and transparency current density of Jtr=26.9 A/cm  and a lower threshold current density of Jth= 78.87 A/cm2  at L=100 A.