Quantum-dot cellular automata (QCA) offer a capable substitute for traditional microelectronics, utilizing quantum mechanics for significantly lower power consumption and enhanced energy efficiency. Adders, essential for arithmetic operations in modern computing, are a key focus within the QCA framework. This work introduces a novel full adder layout featuring a multilayered design with three wire crossings to transfer the binary information in a smooth way without any signal interference. The proposed full adder layout is directly implemented using basic gates and QCA majority voters, not based on a half adder. Compared to previous designs, the proposed layout demonstrates up to a 39% improvement in cell complexity, using three majority gates, thereby being an 83% enhanced design in area-delay cost, proving 56% in area efficiency compared to other relevant designs, indicating the potential for more intricate circuits. The layout was created and simulated using QCADesigner 2.0.3, with total energy estimates reported as 27 meV using QCADesigner-E ver. 2.2. This analysis is crucial and is avoided in most relevant studies. Notably, this energy-efficient design enhances QCA applicability to more complex circuits by eliminating the need for internal nodes. This advancement in scalability marks a significant step forward in higher-order QCA system design.