A method is presented for the solution of Laplace's equation in three dimensions through the use of a combination of polynomial and eigenfunction solutions. Results are presented comparing the method with an exact solution. Excellent agreement is obtained for economical solution representations. The aproximate analytic solution is supplemented by a correction term to ensure that the boundary conditions for the problem are satified exactly. In this form, the method is used to present calculations for the mapping of a hexahedral space to the unit cube.