Large volume cubic press is one of the most popular high pressure devices which can produce pressures up to about 7 GPa. It is well known experimentally that the enhancing of the maximum pressure generated in the large volume cubic press has attracted wide attention among scientists and engineers because the higher pressure is capable of synthesizing some materials with interesting properties. In the large volume cubic press, pyrophyllite is typically used as a pressure-transmitting medium. A specimen immersed in such a solid experiences a generalized stress state. The pressure distribution in pyrophyllite is an important parameter for characterizing the sample environment and designing the experiments at high pressure. There is a need for the quantitative measurement of pressure gradients in the pyrophyllite pressure medium, so that the accurate experimental data under high pressure can be obtained. In the large volume cubic apparatus (68 MN), we put a circuit into the high pressure cubic cell, so that the pressures at various positions can be measured by using the phase transitions in Bi, Tl and Ba. In the present work, the relationship between the total press load and the press load allocated to the anvil face, and the relationship between the total press load and the press load allocated to gaskets are established at room temperature. The results show that with the increase of the total press load, the load allocated to the gaskets is increased sharply, while the curve of load allocated to the anvil face versus total press load reaches a plateau, which results in the cell pressure reaching upper limit when the cell pressure reaches up to about 5 GPa. According to the experimental results, the stress state of the cubic cell under high pressure is analyzed and the reason why the pressure generated in the large volume cubic chamber is difficult to exceed 7 GPa is explained. Based on the geometrical structure of the cubic cell, the scheme to increase the upper pressure limit for cubic cell by using the material with high bulk modulus as the pressure transmitting medium and the material with low bulk modulus as the gasket, is proposed. Additionally, the method of calculating the pressure values at different positions along the axis of symmetry in the cubic cell is given through the quantitative calibration of the pressure gradient in the axial direction of the cubic cell. This method can provide more accurate pressure data for high pressure experiments.