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This paper discusses some interpolation formulas \[u(x_{ * 1} , \cdots ,x_{ * n} ) \simeq \sum _{i = 1}^N {A_i u(v_{i1} , \cdots ,v_{in} )} \] which are exact for all harmonic polynomials in n variables of degrees $\leqq 2$ and $\leqq 3$. The points $(v_{i1} , \cdots ,v_{in} )$ are assumed to lie on the boundary of a region $R_n $ and $(x_{ * 1} , \cdots ,x_{ * n} )$ is in the interior of $R_n $. Thus these formulas can be used to approximate the solution of the Dirichlet problem for $R_n $.