It is widely acknowledged that timely, personalized feedback is necessary for effective and rapid learning, yet providing such feedback at scale remains a challenge in higher education. In this study, we investigate the use of Large Language Models (LLMs) to automate feedback provision within the context of a Database Management Systems (DBMS) course, and we propose a system designed for this purpose. We introduce a feedback mechanism that utilizes GPT-4o to evaluate the SQL queries students write in response to exam questions, generating detailed, individualized critiques of their answers along with confidence indicators. To assess the feasibility of this LLM-centric approach, we conducted a preliminary experimental study using real student exam data. The results show that the GPT-4o-based system can produce feedback closely aligned with instructor evaluations in many cases, offering a promising solution for scaling formative assessment. We outline the design of the system, present observations from the case study, and discuss the potential benefits and challenges of employing LLMs for educational feedback in real-world classroom settings.