Infrared and THz optics has many promising practical applications such as in spectroscopy, diagnostic, optical metrology, sensing, and many others. Due to limited number of IR radiation sources, the frequency down-conversion processes are widely used for obtaining infrared radiation. Among them, the most applicable method is a generation of wave with difference frequency under the three-waves interaction in a medium with quadratic nonlinear response. Below we propose a new effective tool for three times decreasing frequency of the incident pulse based on three-waves interaction in a medium with the quadratic susceptibility. At such interaction, a medium's response inherent cubic non-linearity appears due to so-called cascading SHG. The frequency down-conversion process possesses two stable modes. This is shown using multi-scale method. For each of the modes, the analytical solution is developed in the framework of the long pulse duration approximation without using the pump energy non-depletion approximation. The computer simulation results confirm those of analytical analysis. We show that the conversion efficiency of the incidentpump pulse energy achieves about 70%, if the low frequency wave incident intensity equals zero, or almost 100%, if the incident intensity of the low frequency wave is non-zero. The developed theoretical approach may be applied to other processes of the frequency down-conversion.