Extracellular forces transmitted through the cytoskeleton can deform the cell nucleus. Large nuclear deformation increases the risk of disrupting the nuclear envelope's integrity and causing DNA damage. Mechanical stability of the nucleus defines its capability of maintaining nuclear shape by minimizing nuclear deformation and recovering strain when deformed. Understanding the deformation and recovery behavior of the nucleus requires characterization of nuclear viscoelastic properties. Here, we quantified the decoupled viscoelastic parameters of the cell membrane, cytoskeleton, and the nucleus. The results indicate that the cytoskeleton enhances nuclear mechanical stability by lowering the effective deformability of the nucleus while maintaining nuclear sensitivity to mechanical stimuli. Additionally, the cytoskeleton decreases the strain energy release rate of the nucleus and might thus prevent shape change-induced structural damage to chromatin.