/usr/include/libgdata/gdata/services/youtube/ is in libgdata-dev 0.17.6-2.
This file is owned by root:root, with mode 0o755.
..
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-category.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-comment.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-content.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-credit.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-enums.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-feed.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-query.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-service.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-state.h
/usr/include/libgdata/gdata/services/youtube/gdata-youtube-video.h