Mechanical properties of hierarchically structured nano porous materials are determined by the solid phase stiffness and the pore network morphology. We analyze the mechanical stiffness of hierarchically structured silica monoliths synthesized via a sol gel process, which possess a macroporous scaffold built of interconnected struts with hexagonally ordered cylindrical mesopores. We consider samples with and without microporosity within the mesopore walls and analyze them on the macroscopic level as well as on the microscopic level of the mesopores. Untreated as-prepared samples still containing some organic components and the respective calcined and sintered counterparts of varying microporosity are investigated. To determine Young's moduli on the level of the macroscopic monoliths, we apply ultrasonic run time measurements, while Young's moduli of the mesopore walls are obtained by analysis of the in situ strain isotherms during N-2 adsorption at 77 K. For the latter, we extended our previously reported theoretical approach for this type of materials by incorporating the micropore effects, which are clearly not negligible in the calcined and most of the sintered samples. The comparison of the macro- and microscopic Young's moduli reveals that both properties follow essentially the same trends, that is, calcination and sintering increase the mechanical stiffness on both levels. Consequently, stiffening of the monolithic samples can be primarily attributed to stiffening of the backbone material which is consistent with the fact that the morphology on the mesopore level is mainly preserved with the post-treatments applied.