Is it an infringement for me to put Tagore or Shakespeare's poems on my website for commercial use?

This is the source of the quotation.

Let me make an analogy. If the content you quoted is translated by a publishing house, and the publishing house owns the copyright, then you must be infringing.

If the source is other channels, such as your own translation, and you have not copied other people's content, it is not infringement.