Based on a combination of molecular dynamics simulations, and Raman and Brillouin light scattering spectroscopies, we investigate the structure and elastic properties relationship in an archetypical calcium silicate glass system. From molecular dynamics and Raman spectroscopy, we show that the atomic structure at the short and intermediate length scales is made up of long polymerized silicate chains, which adjusts itself by closing the Si-O-Si angles and leaving more space to [CaO]n edge shared polyhedra to strengthen the glass. Using Brillouin spectroscopy, we observe an increase of elastic constants of the glass with the calcium content, as the cohesion of the glass structure is enhanced through an increase of the binding between the cross-linked calcium-silicate frameworks. This result, albeit being simple in its nature, illustrates for the first time the implication of the calcium framework in the elastic behavior of the glass and will contribute substantially to the understanding of the composition-structure-property relationships in multi-component industrial glasses.