This paper presents a novel data-driven approach for sensing forces for Concentric Tube Continuum Robots. By exploiting their inherent flexibility, the deflection of the robot is used to estimate external forces. This work is based on the usage of a Direct Cascade Architecture of Extreme Learning Machines with Ridge-Regression to estimate the tip contact forces applied to a 6-DoF Concentric Tube Continuum Robots. The introduced incremental learning method achieves a Root-mean-square error of 0.08 N for the whole workspace of the robot with external force magnitudes of less than 0.5 N and an error of 0.0038 N with minor restrictions to the tube rotations with applied force magnitudes of less than 0.1 N.