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We consider a Dirichlet boundary-value problem for the three-dimensional convection-diffusion equations with constant coefficients in the unit cube. A high order compact finite difference scheme is constructed on a 19-point stencil using the Steklov averaging operators. We prove that the finite difference scheme converges in discrete W 2m (ω)-norm with the convergence rate O(hs-m), where the real parameter s satisfies the condition max(1.5, m) < s ≤ m + 4, m = 0, 1, 2, and the exact solution belongs to the Sobolev space W2s (Ω). [ABSTRACT FROM AUTHOR]