Dilute Bose gases interacting through a positive, pairwise, radial potential have a common expression for the first terms of the energy density expansion given by the so-called Lee-Huang-Yang (LHY) formula. The LHY formula depends only on the density of the gas and the scattering length of the potential, showing a universal behavior of the bosonic system independent of the particular shape of the potential. We present a proof of the derivation of the LHY formula in 2D and 3D in thermodynamic regime based on a rigorous Bogoliubov theory and localization techniques. Based on a joint work with S. Fournais, T. Girardot, L. Junge and L. Morin.