Intrinsic evolution of reconfigurable hardware is sought to solve computational problems using the intrinsic processing behavior of System-on-Chip (SoC) platforms. SoC devices combine capabilities of analog and digital embedded components within a reconfigurable fabric under software control. A new technique is developed for these fabrics that leverages the digital resources' enhanced accuracy and signal refinement capability to improve circuit performance of the analog resources' which are providing low power processing and high computation rates. In particular, Differential Digital Correction (DDC) is developed utilizing an error metric computed from the evolved analog circuit to reconfigure the digital fabric thereby enhancing precision of analog computations. The approach developed herein, Cascaded Digital Refinement (CaDR), explores a multi-level strategy of utilizing DDC for refining intrinsic evolution of analog computational circuits to construct building blocks, known as Constituent Functional Blocks (CFBs). The CFBs are developed in a cascaded sequence followed by digital evolution of higher-level control of these CFBs to build the final solution for the larger circuit at-hand. One such platform, Cypress PSoC-5LP was utilized to realize solutions to ordinary differential equations by first evolving various powers of the independent variable followed by that of their combinations to emulate mathematical series-based solutions for the desired range of values. This is shown to enhance accuracy and precision while incurring lower computational energy and time overheads. The fitness function for each CFB being evolved is different from the fitness function that is defined for the overall problem.