We constrain the neutrino-dark matter cross-section using the $13 \pm 5$ neutrino event excess observed by IceCube in 2014-2015, which spatially coincides with the blazar TXS 0506+056. Our analysis take advantage of the dark matter overdensity spike surrounding the supermassive black hole at the blazar's center. To achieve this, we numerically solve the cascade equation, assuming a cross-section that scales with neutrino energy as $\sigma \propto E_{\nu}^n$ for various values of $n$, motivated by different simplified models. We ensure consistency with the IceCube observation by requiring the number of detected events to fall within the 90% confidence interval of the observed $13 \pm 5$ neutrinos. We use the IceCube-adjusted neutrino flux as our reference but also perform calculations with alternative fluxes from studies that incorporate multi-messenger data and are consistent with IceCube's neutrino observations. The resulting constraints are comparable to others derived through similar methodologies.