  We have measured the reflectivity of the optimally doped
Ca$_{8.5}$La$_{1.5}$(Pt$_3$As$_8$)(Fe$_{10}$As$_{10}$) single crystal ($T_c$ =
32.8K) over the broad frequency range from 40 to 12000 $cm^{-1}$ and for
temperatures from 8 to 300 K. The optical conductivity spectra of the low
frequency region ($< 1,000$ $cm^{-1}$) in the normal state (80 K $< T \leq$ 300
K) is well fitted with two Drude forms, which indicates the presence of
multiple bands at the Fermi level. Decreasing temperature below 80 K, this low
frequency Drude spectra develops pseudogap (PG) hump structure at around
$\approx 100$ $cm^{-1}$ and continuously evolves into the fully opened
superconducting (SC) gap structure below $T_c$. Theoretical calculations of the
optical conductivity with the preformed Cooper pair model provide an excellent
description of the temperature evolution of the PG structure above $T_c$ into
the SC gap structure below $T_c$. The extracted two SC gap sizes are $\Delta_S$
= 4.9 $meV$ and $\Delta_L$ = 14.2 $meV$, suggesting
Ca$_{8.5}$La$_{1.5}$(Pt$_3$As$_8$)(Fe$_{10}$As$_{10}$) as a multiple gap
superconductor with a mixed character of the weak coupling and strong coupling
superconductivity.
