The formation of protein mediated DNA loops are a key component in many biological regulatory functions. The binding of LacI protein within the Lac Operon of E.coli serves as the canonical example in which loop regulated transcription is understood. This fundamental looping motif consists of one protein simultaneously bound to two DNA operator binding sites. We calculate the free energy cost of loop formation using a Hamiltonian constructed about the looped state as well as the intrinsically open state of the DNA. The shape of the inter-operator DNA loop in mechanical equilibrium with the protein, is determined using a non-linear mechanical rod model. Our rod model captures the effect of sequence dependent curvature, sequence dependent persistence length, including any anisotropic bending. The equilibrium DNA-protein binding orientations are inferred from LacI protein crystallized with DNA operator segments.Our Hamiltonian describes the change in bending energy of the DNA due to linear perturbations about either the looped or open state. We now calculate the normal modes of the Hamiltonian in order to characterize thermal fluctuations of the loop. Comparing the change stiffness we then calculate the Stockmayer J-factor(looping probability), free energy as well as the entropic contributions, of loop formation. Our works shows that these entropic contributions can play a significant role in determining loop stability and formation.