High-order finite difference schemes suited to super vector-computer are proposed for numerical solution of the three-dimensional Poisson equation. These difference schemes are derived from modification of the right-hand side of the equation. We consider the schemes which are defined on a cube using stencils with the node points which are located on the gridpoints and on the intermediate point between gridpoints. Several high-order difference schemes are examined in view of precision and efficiency. The results exhibit superiority of the new difference scheme in terms of computational efficiency. Moreover it turned out theoretically it is impossible to realize difference schemes of order 8 in the same way.