DNA cyclization is potentially the most powerful approach for systematic quantitation of sequence-dependent DNA bending and flexibility. We extend the statistical mechanics of the homogeneous DNA circle to a model that considers discrete basepairs, thus allowing for inhomogeneity, and apply the model to analysis of DNA cyclization. The theory starts from an iterative search for the minimum energy configuration of circular DNA. Thermodynamic quantities such as the J factor, which is essentially the ratio of the partition functions of circular and linear forms, are evaluated by integrating the thermal fluctuations around the configuration under harmonic approximation. Accurate analytic expressions are obtained for equilibrium configurations of homogeneous circular DNA with and without bending anisotropy. J factors for both homogeneous and inhomogeneous DNA are evaluated. Effects of curvature, helical repeat, and bending and torsional flexibility in DNA cyclization are analyzed in detail, revealing that DNA cyclization can detect as little as one degree of curvature and a few percent change in flexibility. J factors calculated by our new approach are well consistent with Monte Carlo simulations, whereas the new theory has much greater efficiency in computations. Simulation of experimental results has been demonstrated.