The 6 types of poems below need to be unified by a common theme(include the title of poem,author, and theme) 1. A late sixteenth or seventeenth century poem(elizabeth,metaphysica, cavalier) 2.a nineteenth century poem(romantic,gothic,victorian) 3. A twentieth century poem(modern or post modern) 4. A twenty first century poem(post modern) 5. Lyrics to a song 6. A sonnet(or poem written in another traditional form:sestina,terza rima,rondeau,villanelle,etc.)

I think you are asking for examples of poems in all of these genres which are unified by a common theme. In order to find some examples, the easiest thing to do is to consider which themes have historically been used as a focus for poetry, since the earliest times of writing in English. The key themes here are love, death, and God. We can certainly find an example falling into each of these categories for all of these types of poem, but because you have included "Lyrics to a song," we might have better luck focusing on the theme of love: extremely common in poetry and also in popular music.
A love poem for category one, then, might be represented by Andrew Marvell's "The Definition of Love" or "To His Coy Mistress." For category two, a nineteenth century poem, we might suggest a poem by Elizabeth Barrett Browning (perhaps Sonnet 43, "How do I love thee") or Christina Rossetti ("Remember").
For category three, twentieth century poems, we might turn to the love poetry of Sylvia Plath ("Love Letter") or W.H. Auden ("Lullaby"). In terms of twenty-first century poems, it is more difficult here to find a "classic," but certainly poets are still writing on this theme. We might choose Kim Addonizio's "My Heart"--see the citation below for examples of others. For a song lyric, you could choose any popular song about love, but a classic example might be The Beatles' "Can't Buy Me Love." For a sonnet, we could choose Shakespeare's Sonnet 116.
The most important element here is that the same theme, love, has been written about by poets throughout many centuries and using different formats, literary devices and approaches. Because the theme is so timeless, it remains a source of inspiration for poets to approach in their own ways.