To distinguish between the different theories proposed to explain massive star formation, it is crucial to establish the distribution, the extinction, and the density of low-mass stars in massive star-forming regions. We analyze deep X-ray observations of the Orion massive star-forming region using the Chandra Orion Ultradeep Project (COUP) catalog. We studied the stellar distribution as a function of extinction, with cells of 0.03 pc x 0.03 pc, the typical size of protostellar cores. We derived stellar density maps and calculated cluster stellar densities. We found that low-mass stars cluster toward the three massive star-forming regions: the Trapezium Cluster (TC), the Orion Hot Core (OHC), and OMC1-S. We derived low-mass stellar densities of 10^{5} stars pc^{-3} in the TC and OMC1-S, and of 10^{6} stars pc^{-3} in the OHC. The close association between the low-mass star clusters with massive star cradles supports the role of these clusters in the formation of massive stars. The X-ray observations show for the first time in the TC that low-mass stars with intermediate extinction are clustered toward the position of the most massive star, which is surrounded by a ring of non-extincted low-mass stars. This envelope-core structure is also supported by infrared and optical observations. Our analysis suggests that at least two basic ingredients are needed in massive star formation: the presence of dense gas and a cluster of low-mass stars. The scenario that better explains our findings assumes high fragmentation in the parental core, accretion at subcore scales that forms a low-mass stellar cluster, and subsequent competitive accretion. Finally, although coalescence does not seem a common mechanism for building up massive stars, we show that a single stellar merger may have occurred in the evolution of the OHC cluster, favored by the presence of disks, binaries, and gas accretion.