The submesoscale energetics of the eastern Gulf of Mexico (GoM) are diagnosed using outputs from a 1/48° MITgcm simulation. Employed is a recently-developed, localized multiscale energetics formalism with three temporal scale ranges (or scale windows), namely, a background flow window, a mesoscale window, and a submesoscale window. It is found that the energy cascades are highly inhomogeneous in space. Over the eastern continental slope of the Campeche Bank, the submesoscale eddies are generated via barotropic instability, with forward cascades of kinetic energy (KE) following a weak seasonal variation. In the deep basin of the eastern GoM, the submesoscale KE exhibits a seasonal cycle, peaking in winter, maintained via baroclinic instability, with forward available potential energy (APE) cascades in the mixed layer, followed by a strong buoyancy conversion. A spatially-coherent pool of inverse KE cascade is found to extract energy from the submesoscale KE reservoir in this region to replenish the background flow. The northern GoM features the strongest submesoscale signals with a similar seasonality as seen in the deep basin. The dominant source for the submesoscale KE during winter is from buoyancy conversion and also from the forward KE cascades from mesoscale processes. To maintain the balance, the excess submesoscale KE must be dissipated by smaller-scale processes via a forward cascade, implying a direct route to fine-scale dissipation. Our results highlight that the role of submesoscale turbulence in the ocean energy cycle is region- and time-dependent.