Abstract Recent studies in different types of galaxies reveal that the product of the central density and the core radius (ρcrc) is a constant. However, some empirical studies involving galaxy clusters suggest that the product ρcrc depends weakly on the total dark halo mass. In this Letter, we re-analyse the hot gas data from 106 clusters and obtain a surprisingly tight scaling relation: $\rho _{\rm c} \propto r_{\rm c}^{-1.46 \pm 0.16}$. This result generally agrees with the claims that ρcrc is not a constant for all scales of structure. Moreover, this relation does not support the velocity-dependent cross-section of dark matter if the core formation is due to the self-interaction of dark matter.