Tumorigenesis induces actin cortex remodeling, which makes cancerous cells softer. Cell deformability is largely determined by myosin-driven cortical tension and actin fiber architecture at the cell cortex. However, it is still unclear what the weight of each contribution is, and how these contributions change during cancer development. Moreover, little attention has been paid to the effect of energy metabolism on this phenomenon and its reprogramming in cancer. Here, we perform precise two-dimensional mechanical phenotyping based on power-law rheology to unveil the contributions of myosin II, actin fiber architecture and energy metabolism to the deformability of healthy (MCF-10A), noninvasive cancerous (MCF-7), and metastatic (MDA-MB-231) human breast epithelial cells. Contrary to the perception that the actin cortex is a passive structure that provides mechanical resistance to the cell, we find that this is only true when the actin cortex is activated by metabolic processes. The results show marked differences in the nature of the active processes that build up cell stiffness, namely that healthy cells use ATP-driven actin polymerization whereas metastatic cells use myosin II activity. Noninvasive cancerous cells exhibit an anomalous behavior, as their stiffness is not as affected by the lack of nutrients and ATP, suggesting that energy metabolism reprogramming is used to sustain active processes at the actin cortex.