Based on earlier papers of the first author we give a concise formula for the values of class zeta functions of totally real cubic fields at even positive integers which is the exact analogue of the Barn-Siegel formula for real quadratic fields. For this purpose we use a rather complicated series representation for the aforementioned values depending on a parameter x which is analyzed for x → 0. The final formula is well suited for actual computations; two tables of values of class zeta functions are given at the end of the paper.
