Sonnet 60 keeps its discussion of art and culture short—the only real clear reference to this theme comes in the last two lines, in the reference to the speaker's "verse." That said, this brief reference says it all. And then some. The speaker presents his work as an artist or craftsman as a way of opposing the destructive forces of nature. So long as his verse remains in existence, he will be able to continue praising his beloved. Even if most of the concrete details of Shakespeare's life remain shrouded in mystery, it is undeniable that some part of him lives on through his work. Now that's art.
The speaker suggests that art can provide some limited consolation for death. But hey, some consolation is better than none at all, right?
The speaker uses literary allusions to signal his disagreement with standard Christian belief. Zing!