Low cost scintillation detectors as compared with HPGe detectors are considered to be one of most important radiation detection tools. Therefore, these detectors can be manufactured in different shapes and work at room temperature without any cooling systems, which added an extra advantage to it. This work presents a study of a cubic detector with a rectangular cavity in different experimental setup geometries, using standard point-like gamma-ray sources, where the efficiency of the detector in these geometries was the target to be studied. According to this aim, the data from the experimental measurements was used to determine the detector efficiency. An analytical calculation of the detector efficiency was done by using a new mathematical expression, this mathematical expression depends on the efficiency transfer technique and effective solid angle calculations. To support the mathematical model, the source-to-detector arrangement was simulated by Geant4 Monte Carlo code. All the compared efficiency results were found to be promising and trusted based on the calculated deviation percentages.