Translating culture-related content is vital for effective cross-cultural communication. However, many culture-specific items (CSIs) often lack literal translation across languages, making it challenging to collect high-quality, diverse parallel corpora with CSI annotations. This difficulty hinders the analysis of cultural awareness of machine translation (MT) systems, including traditional neural MT and the emerging MT paradigm using large language models (LLM). To address this gap, we introduce a novel parallel corpus, enriched with CSI annotations in 6 language pairs for investigating Cultural-Aware Machine Translation—CAMT. Furthermore, we design two evaluation metrics to assess CSI translations, focusing on their pragmatic translation quality. Our findings show the superior ability of LLMs over neural MTs in leveraging external cultural knowledge for translating CSIs, especially those lacking translations in the target culture.