In very high energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, , is equal to , where is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we perform a non--perturbative numerical computation of the function . It decreases rapidly for small but varies only by %, from to , for a wide range 35.36--296.98 in , including the range relevant for collisions at RHIC and LHC. Extrapolating to SU(3), we estimate the initial energy per unit rapidity for Au-Au collisions in the central region at RHIC and LHC.