This paper addresses resource allocation for sum throughput maximization in a sectorized two-cell downlink orthogonal frequency-division multiple-access (OFDMA) system impaired by multicell interference. It is well known that the optimization problem for this scenario is NP-hard and combinational, which is here converted to a novel sum throughput maximization problem in cellular OFDMA systems based on the intercell interference limitation. Then, three subclasses of this new problem are solved. By the first subclass, on the assumption that subcarrier allocation parameters are fixed, an algorithm for optimal power allocation is obtained. However, the optimal resource allocation requires an exhaustive search, including the optimal power allocation which cannot be implemented in practice due to its high complexity. By the second subclass, the problem is reduced to a single cell case where the intercell interference in each subcarrier is limited to a certain threshold. Based on the solution of the single cell problem, a distributed resource allocation scheme with the aim of small information exchange between the coordinated base stations is proposed. By the third subclass, the centralized resource allocation for two adjacent cells as a general problem is solved. Here, the algorithm allocates simultaneously the subcarriers and the power of the considered two cells while the resource allocation parameters of both cells are coupled mutually. The present study shows that distributed and centralized resource allocation algorithms have much less complexity than the algorithm used in the exhaustive search and can be used in practice as efficient multicell resource allocation algorithms. Simulation results illustrate the performance improvements of the proposed schemes in comparison to the schemes with no intercell interference consideration.