This study investigates the effect of encapsulating a golden fullerene (Au32) cluster on the mechanical properties of a single-walled carbon nanotube (SWCNT) and a boron-nitride nanotube (BNNT). First, the geometrical parameters of the nanopeapods were optimized using the density functional theory (DFT) method. The DFT results demonstrated that the strength of interaction between the Au32 cage and a BNNT was stronger than that between the Au32 cage and SWCNT. The molecular dynamics (MD) method was then applied to calculate mechanical properties such as Young’s modulus, failure stress, and failure strain using a stress–strain plot. The mechanical results indicated that encapsulating the Au32 cluster reduced the Young’s modulus and failure stress of both a SWCNT and BNNT, whereas the failure strain did not observably change. To validate these results, a C60 cage was inserted inside an SWCNT in the most exothermic situation. The MD calculation indicated that, similar to the effect of Au32 in the Au32-nanotube peapod, C60 reduced the mechanical properties of the SWCNT.