Biological systems are intrinsically robust. The system, being an open one, is permanently exposed to perturbations due to external noise from the surrounding environment. In this context, the architecture and information processing capabilities of a signaling network play an important role in attenuating the noise. Multi-layered phosphorylation cascades are architectures prevalent in some of our major signaling pathways. In this work, we investigate the robustness of such signaling cascades with respect to external input variations. We employ local sensitivity and output-variance based sensitivity as measures of robustness for such cascades and observe that the efficiency of high frequency signal attenuation increases with the number of in the cascades. Filtering properties of cascades have been observed previously but not under a very rigorous theoretical framework and not in comparison with other models. This work provides an example of optimality versus robustness tradeoff in the design principles of biological systems.