Large language models (LLMs) have achieved strong performance in general machine translation, yet their ability in culture-aware scenarios remains poorly understood. To bridge this gap, we introduce CanMT, a Culture-Aware Novel-Driven Parallel Dataset for Machine Translation, together with a theoretically grounded, multi-dimensional evaluation framework for assessing cultural translation quality. Leveraging CanMT, we systematically evaluate a wide range of LLMs and translation systems under different translation strategy constraints. Our findings reveal substantial performance disparities across models and demonstrate that translation strategies exert a systematic influence on model behavior. Further analysis shows that translation difficulty varies across types of culture-specific items, and that a persistent gap remains between models' recognition of culture-specific knowledge and their ability to correctly operationalize it in translation outputs. In addition, incorporating reference translations is shown to substantially improve evaluation reliability in LLM-as-a-judge, underscoring their essential role in assessing culture-aware translation quality. The corpus and code are available at CanMT.