BurstCube is a 6U CubeSat (10 x 20 x 30 cm) designed to rapidly detect and disseminate information about gamma-ray bursts (GRBs) to both expand sky coverage and supplement existing observatories. To do this, the mission requires a lightweight yet robust data processing pipeline system which can be easily deployed, requires minimal maintenance, can perform standard gamma-ray burst analysis to convert raw instrument data to FITS standard data files, and can handle transfers to science archiving and alert systems. This is accomplished via a three-stage processing pipeline consisting of Level 0, Level 1, and Level 2 (L0, L1, and L2) processing routines. These stages convert data from the instrument transmitted in CCSDS Space packet format to FITS file format, perform event localization, generate light curves and spectra, perform automated event classification, and disseminate rapid detection alerts and related event information to the community via the GCN to allow multi-wavelength and multi-messenger follow-ups by other observatories. Processed event data and ancillary data products are then transferred to and served to the public via the HEASARC at Goddard Space Flight Center. In this poster the software architecture of the BurstCube Data Analysis Pipeline is detailed, including individual data levels, the processing tasks involved, and interactions with data archiving and science alert systems.