Cross-border interconnection and trade (CBIT) can effectively leverage the differences in resource endowments and energy demand between regions and countries, making cross-border cooperation a potential option for addressing the high penetration of variable renewable energy. This paper presents centralized and decentralized planning approaches for the cross-border energy transmission expansion planning (TEP) problem. The proposed centralized mixed-integer second-order cone programming (MISOCP) model collaboratively optimizes the expansion of national energy networks, while considering the impact of CBIT. To protect the privacy of energy data in each country, the alternating direction method of multipliers (ADMM) algorithm is extended to decompose the centralized optimization formulation into mutually independent sub-optimization issues, and adaptively adjust the penalty parameters and Lagrangian multipliers to improve convergence. This study also quantifies the effect of cross-border cooperation in such co-expansion problems as a comparative consideration. Numerical simulations on the modified cross-border integrated energy network validates the correctness and effectiveness of the proposed model and solution methodology. The results show that cross-border cooperation can reduce a country's internal energy network congestion, thus postponing the expansion investment decisions. It also shows that the distributed coordinated planning is more efficient in terms of lower cost and renewable generation curtailment that than independent optimization method. Therefore, cross-border collaboration brings economic, environmental, and renewable integration benefits to interconnected countries.