The terms which are proportional to the cube of the density in the expansions of the pair distribution function g(r), and the direct correlation function c(r), have been evaluated for the 6 : 12 potential. In addition, these terms have been evaluated using the Percus-Yevick (PY), hyper-netted chain (HNC), PY2, and HNC2 theories. Comparison of these approximate and exact values for g(r) and c(r) and of the resulting approximate and exact values of the fifth virial coefficient shows that, to this order in the density, the PY2 and HNC2 theories are very reliable. Extensions of the PY and HNC theories which are simpler thean the PY2 and HNC2 theories are also considered.