The radio luminosity functions (RLFs) of active galactic nuclei (AGNs) are traditionally measured based on total emission, which does not reflect the current activity of the central black hole. The increasing interest in compact radio cores of AGNs motivates determination of the RLF based on core emission (i.e., core RLF). In this work we have established a large sample (totaling 1207) of radio-loud AGNs, mainly consisting of radio galaxies (RGs) and steep-spectrum radio quasars (SSRQs). Based on the sample, we explore the relationship between core luminosity (L-c) and total luminosity (L-t) via a powerful statistical tool called "Copula." The conditional probability distribution p(log L-c| log L-t) is obtained. We derive the core RLF as a convolution of p(log L-c| log L-t) with the total RLF that was determined by previous work. We relate the separate RG and SSRQ core RLFs via a relativistic beaming model and find that SSRQs have an average Lorentz factor of gamma = 9.84(-2.50)(+3.61), and that most are seen within 8 degrees less than or similar to theta less than or similar to 45 degrees of the jet axis. Compared with the total RLF, which is mainly contributed by extended emission, the core RLF shows a very weak luminosity-dependent evolution, with the number density peaking around z. similar to. 0.8 for all luminosities. Differences between core and total RLFs can be explained in a framework involving a combination of density and luminosity evolutions where the cores have significantly weaker luminosity evolution than the extended emission.