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We have investigated the protostellar disk around a Class 0/I protostar, L1527 IRS, using multi-wavelength observations of the dust continuum emission at $λ=0.87$, 2.1, 3.3, and 6.8 mm obtained by the Atacama Large Millimeter/submillimeter Array (ALMA) and the Jansky Very Large Array (VLA). Our observations achieved a spatial resolution of $3-13$ au and revealed an edge-on disk structure with a size of $\sim80-100$ au. The emission at 0.87 and 2.1 mm is found to be optically thick within a projected disk radius of $ r_{\rm proj}\lesssim50$ au. The emission at 3.3 and 6.8 mm shows that the power-law index of the dust opacity ($β$) is $β\sim1.7$ around $ r_{\rm proj}\sim 50$ au, suggesting that grain growth has not yet begun. The dust temperature ($T_{\rm dust}$) shows a steep decrease with $T_{\rm dust}\propto r_{\rm proj}^{-2}$ outside of the VLA clumps previously identified at $r_{\rm proj}\sim20$ au. Furthermore, the disk is gravitationally unstable at $r_{\rm proj}\sim20$ au, as indicated by a Toomre {\it Q} parameter value of $Q\lesssim1.0$. These results suggest that the VLA clumps are formed via gravitational instability, which creates a shadow on the outside of the substructure, resulting in the sudden drop in temperature. The derived dust masses for the VLA clumps are $\gtrsim0.1$ $M_{\rm J}$. Thus, we suggest that Class 0/I disks can be massive enough to be gravitationally unstable, which might be the origin of gas-giant planets in a 20 au radius. Furthermore, the protostellar disks can be cold due to shadowing.