/u/Bacarruda is correct to point out the importance of the National Endowment for the Arts and the National Endowment for the Humanities. Both of these grew out of legislation passed in 1965 at the request of former First Lady Jacqueline Kennedy. This was part of her effort to secure a cultural legacy in remembrance of the Kennedy administration. As indicated in a separate thread here, neither are formally part of the cabinet, but both agencies answer directly to the President.

Another law that the First Lady advocated with the National Historic Preservation Act (NHPA) of 1966, which raised the profile of preservation by creating an aggressive program within the National Park System: the National Register Program consolidated the National Historic Landmarks, which dated to the 1930s, and created a branch of the Park Service that included documentation, recognition, grants , and technical services. Over the years, there have been efforts to remove the National Register Program from the National Park Service; advocates have felt it is lost in the larger agency, while those who argue for the status quo point out that it could be an easy target for budget cuts if it were a small, "stand-alone" answering directly to the president. As part of the NHPA of 1966, the law called for the creation of the Advisory Council for Historic Preservation, which is an overview agency designed to ensure that federal agencies comply with the NHPA, and this Council also answers directly to (and is appointed by) the president.

The newest agency to further the advancement of culture is the Institute for Museums and Library Services, which like the Arts and the Humanities, is not formally in the cabinet, but which does answer directly to the president.

edit: just a note to address the two organizations that /u/nerga mentions: the Smithsonian is not technically in the executive branch, but rather stands apart from the federal government, receiving federal support, but functioning more like a non-profit organization. It is a federal establishment that is not technically in any of the three branches of government. The Library of Congress is an agency of Congress (hence the name), and so it is also removed from the executive branch and any relationship with the cabinet. But it was good of /u/nerga to point out those two institutions.

It does.. In fact, it has two agencies.