Drug synergy prediction is a challenging and important task in the treatment of complex diseases including cancer. In this manuscript, we present a novel unified Model, known as BAITSAO, for tasks related to drug synergy prediction with a unified pipeline to handle different datasets. We construct the training datasets for BAITSAO based on the context-enriched embeddings from Large Language Models for the initial representation of drugs and cell lines. After demonstrating the relevance of these embeddings, we pre-train BAITSAO with a large-scale drug synergy database under a multi-task learning framework with rigorous selections of tasks. We demonstrate the superiority of the model architecture and the pre-trained strategies of BAITSAO over other methods through comprehensive benchmark analysis. Moreover, we investigate the sensitivity of BAITSAO and illustrate its unique functions including new drug discoveries, drug combinations-gene interaction, and multi-drug synergy predictions.