In nature, animals often need to move/manipulate objects comparable in weight/size to their own bodies. Compared to grasping and carrying, pushing provides a more straightforward and efficient non-prehensile manipulation strategy, avoiding complex grasp design while leveraging direct contact to regulate an object's pose during interaction. Achieving effective pushing, however, requires both sufficient manipulation capability and stable whole-body coordination, which is particularly challenging when dealing with heavy or irregular objects. To address these challenges, we propose HeLoM, a learning-based hierarchical whole-body manipulation framework for hexapod robots that exploits coordinated multi-limb control and is applicable to multi-legged robotic systems. Inspired by the cooperative strategies of multi-legged insects, our framework leverages multiple contact points and high degrees of freedom to enable efficient and dynamic whole-body coordination during object interaction. HeLoM's high-level planner plans pushing behaviors, while its low-level controller maintains locomotion stability and generates dynamically consistent joint actions. This design enables the robot to maintain balance while executing continuous and controllable pushing behaviors through coordinated foreleg interaction and supportive hind-leg propulsion. We validate the effectiveness of HeLoM through both simulation and real-world experiments. Results show that our framework can stably push objects of varying sizes and unknown physical properties to designated goal poses in the real world.