The design of high-performance, lightweight materials has always been challenging in aerospace structural design (e.g., aircraft ailerons, flaps, and rudders). Sandwich panel composites with lattice cores are widely used in aerospace applications. This paper presents an inverse design optimization framework for sandwich structures with implicitly represented architected cellular unit cells. Specifically, cellular materials are implicitly represented (described by functions) as building blocks in the core structure design. A core topology optimization problem is formulated based on functionalities (compliance and thermal conductivity) in this paper. Lastly, the optimized delicate design is directly converted into digital slices for additive manufacturing, which avoids memory-expensive solid model conversion. The proposed design framework is validated in two aerospace design case studies. Experimental results demonstrate the effectiveness of the proposed optimization algorithm and STL-free scheme for additive manufacturing.