Dielectric photonics platform provides unique possibilities to control light scattering via utilizing high-index dielectric nanoantennas with peculiar optical signatures. Despite the intensively growing field of all-dielectric nanophotonics, it is still unclear how surrounding media affect scattering properties of a nanoantenna with complex multipole response. Here, we report on light scattering by a silicon cubic nanoparticle embedded in lossless media, supporting optical resonant response. We show that significant changes in the scattering process are governed by the electro-magnetic multipole resonances, which experience spectral red-shift and broadening over the whole visible and near-infrared spectra as the indices of media increase. Most interestingly, the considered nanoantenna exhibits the broadband forward scattering in the visible and near-infrared spectral ranges due to the Kerker-effect in high-index media. The revealed effect of broadband forward scattering is essential for highly demanding applications in which the influence of the media is crucial such as health-care, e.g., sensing, treatment efficiency monitoring, and diagnostics. In addition, the insights from this study are expected to pave the way toward engineering the nanophotonic systems including but not limited to Huygens-metasurfaces in media within a single framework.