We propose a novel multi-section cable-driven soft robotic arm inspired by octopus tentacles along with a new modeling approach. Each section of the modular manipulator is made of a soft tubing backbone, a soft silicon arm body, and two rigid endcaps, which connect adjacent sections and decouple the actuation cables of different sections. The soft robotic arm is made with casting after the rigid endcaps are 3D-printed, achieving low-cost and convenient fabrication. To capture the nonlinear effect of cables pushing into the soft silicon arm body, which results from the absence of intermediate rigid cable guides for higher compliance, an analytical static model is developed to capture the relationship between the bending curvature and the cable lengths. The proposed model shows superior prediction performance in experiments over that of a baseline model, especially under large bending conditions. Based on the nonlinear static model, a kinematic model of a multi-section arm is further developed and used to derive a motion planning algorithm. Experiments show that the proposed soft arm has high flexibility and a large workspace, and the tracking errors under the algorithm based on the proposed modeling approach are up to 52$\%$ smaller than those with the algorithm derived from the baseline model. The presented modeling approach is expected to be applicable to a broad range of soft cable-driven actuators and manipulators.