The aim of this paper is to propose efficient algorithms for computing the energetic lower bounds of the cumulative sheduling problem. So we have to schedule in a minimal makespan a set of non preemptive tasks on a resource with a given capacity. A task has a release date, a processing time and a tail and requires a given amount of the resource capacity during its processing. The energetic lower bound is the largest value of the makespan such that the energetic reasoning check cannot detect unfeasability. We report some algorithms to practically compute this lower bound with efficient complexity. These algorithms rely on iterative augmentations of Cmax until the cumulative constraint or the energetic constraint is satisfied. Our Computational results show their practical efficiencies.