We present 500 and 700au resolution 1 and 3mm Atacama Large Millimeter/submillimeter Array observations, respectively, of protostellar cores in protoclusters Sagittarius B2 (Sgr B2) North (N) and Main (M), parts of the most actively star-forming cloud in our Galaxy. Previous lower-resolution (5000au) 3mm observations of this region detected ~150 sources inferred to be young stellar objects (YSOs) with M>8M_{sun}_. With a 10-fold increase in resolution, we detect 371 sources at 3mm and 218 sources in the smaller field of view at 1mm. The sources seen at low resolution are observed to fragment into an average of two objects. About one-third of the observed sources fragment. Most of the sources we report are marginally resolved and are at least partially optically thick. We determine that the observed sources are most consistent with Stage 0/I YSOs, i.e., rotationally supported disks with an active protostar and an envelope, that are warmer than those observed in the solar neighborhood. We report source-counting-based inferred stellar mass and the star formation rate of the cloud: 2800M_{sun}_ and 0.0038M_{sun}_/yr for Sgr B2 N and 6900M_{sun}_ and 0.0093M_{sun}_/yr for Sgr B2 M, respectively.