This work presents a comprehensive analytical model to predict global and local buckling modes in sandwich columns with additively manufactured Face-Centered Body-Centered Cubic (FBCC) lattice cores and aluminium facesheets. Global buckling (out-of-plane and in-plane) and local failure modes such as intracell buckling and wrinkling are analyzed using a combination of existing and newly proposed methods. A novel higher-order closed-form analytical solution is specifically developed for the symmetrical wrinkling mode, incorporating transverse compressibility and shear deformation through refined displacement fields, enabling improved prediction accuracy. Finite Element Method (FEM) simulations using 3D solid and beam elements validate the analytical results across four boundary conditions: Fixed-Fixed, Fixed-Pinned, Pinned-Pinned, and Fixed-Free. The study demonstrates excellent agreement between analytical and numerical results, particularly for wrinkling, which is shown to be independent of boundary conditions. The analysis also identifies a transition between intracell buckling and wrinkling depending on facesheet and core thickness. The comprehensive model integrates Allen’s thin/thick face formulas for global buckling, Zenkert’s expression for intracell buckling, and the newly proposed higher-order formulation for wrinkling. The final framework allows efficient prediction of the dominant failure mode based on minimum critical load and offers a robust and computationally efficient tool for sandwich column with lattice core stability analysis.