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Compact formulas are obtained for the Casimir energy of a relativisticperfect fluid confined to a $D$-dimensional hypercube with von Neumann orDirichlet boundary conditions. The formulas are conveniently expressed as afinite sum of the well-known gamma and Riemann zeta functions. Emphasis isplaced on the mathematical technique used to extract the Casimir energy from a$D$-dimensional infinite sum regularized with an exponential cut-off. Numericalcalculations show that initially the Dirichlet energy decreases rapidly inmagnitude and oscillates in sign, being positive for even $D$ and negative forodd $D$. This oscillating pattern stops abruptly at the critical dimension ofD=36 after which the energy remains negative and the magnitude increases. Weshow that numerical calculations performed with 16-digit precision areinaccurate at higher values of $D$.Comment: 20 pages, 4 figure

Casimir energy of a relativistic perfect fluid confined to a D-dimensional hypercube