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The pre-computation of data cubes is critical for improving the response time of OLAP(On-Line Analytical Processing) systems. In order to meet the need for improved performance created by growing data sizes, parallel solutions for data cube construction are becoming increasingly important. This paper presents two parallel methods for data cube construction based on an extendible multidimensional array, which is dynamically extendible along any dimension without relocating any existing data. We have implemented and evaluated our core-based parallel data cube construction methods on shared-memory multiprocessors. Given the performance limit, the methods achieve close to linear speedup with load balance. Our experiments also indicate that our parallel methods can be more scalable on higher dimensional data cube construction.