Video summarization aims to create short, accurate, and cohesive summaries of longer videos. Despite the existence of various video summarization datasets, a notable limitation is their limited amount of source videos, which hampers the effective fine-tuning of advanced large vision-language models (VLMs). Additionally, most existing datasets are created for video-to-video summarization, overlooking the contemporary need for multimodal video content summarization. Recent efforts have been made to expand from unimodal to multimodal video summarization, categorizing the task into three sub-tasks based on the summary's modality: video-to-video (V2V), video-to-text (V2T), and a combination of video and text summarization (V2VT). However, the textual summaries in previous multimodal datasets are inadequate. To address these issues, we introduce Instruct-V2Xum, a cross-modal video summarization dataset featuring 30,000 diverse videos sourced from YouTube, with lengths ranging from 40 to 940 seconds and an average summarization ratio of 16.39\%. Each video summary in Instruct-V2Xum is paired with a textual summary that references specific frame indexes, facilitating the generation of aligned video and textual summaries. In addition, we propose a new video summarization framework named V2Xum-LLM. V2Xum-LLM, specifically V2Xum-LLaMA in this study, is the first framework that unifies different video summarization tasks into one large language model's (LLM) text decoder and achieves task-controllable video summarization with temporal prompts and task instructions. Experiments show that V2Xum-LLaMA outperforms strong baseline models on multiple video summarization tasks. Furthermore, we propose an enhanced evaluation metric for V2V and V2VT summarization tasks.