Due to the low computational cost, nodal diffusion methods are still commonly used to simulate full-core reactor problems. This work represents the developmental effort to build an accurate nodal kernel to treat hexagonal geometry in the core simulator code PARCS. An innovative method called TriPEN-9 has been developed by splitting a hexagonal assembly into six triangular nodes and solved using cubic polynomial expansion for the scalar flux with nine-term expansion coefficients. The nodal diffusion calculation is further accelerated with the multilevel coarse-mesh finite difference method. The verification of the TriPEN-9 method on the VVER full-core problem is provided with the model based on the NURESIM (Nuclear Reactor Simulator)-SP1 V1000-2D-C1-tr benchmark problem. The Serpent Monte Carlo code is used as a reference solution for verification and to generate homogenized group-constants data for PARCS. Exact discontinuity factors were generated in GenPMAXS, a cross-section processing code, using a similar expansion method as the TriPEN-9 core solver method with the utilization of heterogeneous solutions from Serpent. Implementing the TriPEN-9 method in PARCS, this approach can exactly reproduce the solutions from the high-fidelity Serpent calculations.