While there can be cultural contexts in poetry, this is often abstract in delivery and meaning making it difficult to determine if it is a factual record of history or the poet's perception of this. For me, the answer to this question is a combination of the two.
To quote from Aristotle, ‘History reports what happened and is therefore subject to all the constraints and imperfections of actual life, while poetry uses words in their fuller potential, creating representations that are more complete and meaningful than nature can give us in the raw.’
Poetry predates literacy as an oral history employed to remember and pass down family history, events, genealogy, and law. Many of the poems surviving from ancient times form of a record of cultural information about the people of the past, religious subject matter, politics and wars and the myths of their societies that formed its structure.
Postmodernists claim all experience of the world is with and through language, although this concept is difficult to accept since some experiences have more to do with bodily physiology and social usage, therefore cannot be readily conveyed in words.
The cultural context of poetry from different countries is not always about the history of that place. Many eastern forms of poetry, traditional haiku, for example, frequently focus on natural themes or images, while tankas are often used to describe the human condition in relation to place.
However, language in poetry certainly influences our perceptions and responses because of the intentions, associations and histories of usage that employs the traditional resources of language. This is separate to the forms of poetry, which are more than ornamental to impart a more exact commentary and expressive power. Looking beneath the pattern or prescribed form, poetry attempts to tell the truth in a fuller and more authentic manner. The language of poetry illuminates truth and sharpens perception and understanding. It heightens the emotional experience of history.
Poetry enables us to see life, past and present, with clarity and understanding. It reconciles us to the visible incongruities, injustices and the brutalities of our natures. In poetry we learn to see life as it is directly given to us through timeless ideas.
William Blake used poetry as an ideological weapon raised in defiance against the establishment, and in doing so contributed to social change, while others such as Whitman in America and Lawson in Australia recorded the social and economic history of their time.
The two cultural contexts in, To His Coy Mistress by Andrew Marvell, can be interpreted as an allegory for political rebellion and the challenging of traditional beliefs about female sexuality. As such it provides a factual history of the conventional beliefs in mid-17th century England. This contrasts with The Fish by Elizabeth Bishop, which is more an insight into a personal history within a specific culture.
So I see poetry as providing a combination of record of factual history and the poet’s perception of events as seen through their own experience, a truth, but not necessarily a shared truth. One thing is certain, however, without poetry the world would be a poorer place for the knowledge we have gained from it about the past and the people who lived before us.