  Spherical confinement in 3D harmonic, quartic and other higher oscillators of
even order is studied. The generalized pseudospectral method is employed for
accurate solution of relevant Schr\"odinger equation in an \emph{optimum,
non-uniform} radial grid. Eigenvalues, eigenfunctions, position expectation
values, radial densities in \emph{low and high-lying} states are presented in
case of \emph{small, intermediate and large} confinement radius. The
\emph{degeneracy breaking} in confined situation as well as correlation in its
\emph{energy ordering} with respect to the respective unconfined counterpart is
discussed. For all instances, current results agree excellently with best
available literature results. Many new states are reported here for first time.
In essence, a simple, efficient method is provided for accurate solution of 3D
polynomial potentials enclosed within spherical impenetrable walls.
