  In this paper, the first order radiative correction to the Casimir energy for
a massive scalar field in the $\phi^4$ theory on a spherical surface with $S^2$
topology was calculated. In common methods for calculating the radiative
correction to the Casimir energy, the counter-terms related to free theory are
used. However, in this study, by using a systematic perturbation expansion, the
obtained counter-terms in renormalization program were automatically
position-dependent. We maintained that this dependency was permitted,
reflecting the effects of the boundary conditions imposed or background space
in the problem. Additionally, along with the renormalization program, a
supplementary regularization technique that we named Box Subtraction Scheme
(BSS) was performed. This scheme presents a useful method for the
regularization of divergences, providing a situation that the infinities would
be removed spontaneously without any ambiguity. Analysis of the necessary
limits of the obtained results for the Casimir energy of the massive and
massless scalar field confirmed the appropriate and reasonable consistency of
the answers.
