  We employ the numerical linked-cluster expansion to study finite-temperature
properties of the uniform cubic lattice Hubbard model in the thermodynamic
limit for a wide range of interaction strengths and densities. We carry out the
expansion to the 9th order and find that the convergence of the series extends
to lower temperatures as the strength of the interaction increases, giving us
access to regions of the parameter space that are difficult to reach by most
other numerical methods. We study the precise trends in the specific heat, the
double occupancy, and magnetic correlations at temperatures as low as 0.2 of
the hopping amplitude in the strong-coupling regime. We show that in this
regime, accurate estimates for transition temperatures to the N\'{e}el ordered
phase, in agreement with the predicted asymptotic behavior, can be deduced from
the low-temperature magnetic structure factor. We also find evidence for
possible instability to the magnetically ordered phase away from, but close to,
half filling. Our results have important implications for parametrizing
fermionic systems in optical lattice experiments and for benchmarking other
numerical methods.
