There's this bit from one of Lord Byron's poems:
When Bishop Berkeley said "there was no matter,"And Berkeley pops up in two poems by W. B. Yeats: 'The Seven Sages' and 'Blood and the Moon'.
And proved it—'twas no matter what he sald:
They say his system 'tis in vain to batter,
Too subtle for the airiest human head (from Don Juan, Canto 11)
And God-appointed Berkeley that proved all things a dream,All of these poems are noted by Breidert.
That this pragmatical, preposterous pig of a world, its farrow that so solid seem,
Must vanish on the instant if the mind but change its theme (from 'Blood & the Moon', 1928)
Breidert doesn't discuss poetic invocations of David Hume, but my own googling has turned up few lyrical mentions of the great skeptic. Poor Hume is 'ungrateful Hume' in a poem about whist (Whist: a poem in twelve cantos by Alexander Thomson, 1791); and, in a poem written upon his demise, Hume is condemned as 'the modern Midas' ('On the Death of David Hume' by William Julius Mickle, 1776) chiefly because he had bad-mouthed Spenser's poetry. Thomas Blacklock sang Hume's praises but that doesn't count -- Blacklock was impoverished and received financial support from Hume.
Granted, Paul Muldoon's Madoc: a Mystery has sections headed 'Berkeley' and 'Hume' (and 'Kant', and 'Frege', and 'Meinong', and 'Husserl', and 'Putnam', etc.etc.), but those headings seem to have little to do with the poetry.
Percy Bysshe Shelley was inspired by Hume but seems not to have let this show in his poetry. Was Hume too toxic even in Shelley's day? If so, couldn't Shelley have fit Hume into a private poem (with an eye to posthumous publication)?
If I'm not mistaken, Berkeley has had more attention from the poets than most other early modern philosophers. Is the attraction due to his philosophical views? If so, one would expect Hume to have featured in more poems owing to the similarity between his and Berkeley's ideas. Or does Berkeley get the poetic limelight because he drew Dr. Johnson's ire?
Update (June 22, 2014): Byron's Don Juan is loaded with philosophers. Locke's referred to in the 15th and the 17th cantos. Other philosophers in the poem are Socrates, Plato, Aristotle, Rousseau, Machiavelli, both Bacons (Francis and Roger), and 'Professor Kant'. No Hume, though. I guess in Byron's time, Hume was primarily remembered (if at all) as a historian rather than as a philosopher (even though it was Hume's philosophy that influenced Shelley).
Here's a nifty site where you can enter searches for "poems about...." For example, poems about Kant, about Hegel, and about Hume. Only 6 of the 10 search results for Hume are about David Hume. Four of the remaining poems are of little interest and two are by George Crabbe. Hume gets no love from the poets. I don't see Thomson's, Mickle's, or Blacklock's lyrics among the search results.
Update (June 23, 2014): John Koethke mentions Hume in a poem called 'The Constant Voice' (2002), which has a line about Hume on sympathy. Koethke's a philosophy professor. (In 'Like Gods' Koethke refers to David Lewis and Frank Jackson. Koethke's 'Book X' is about Plato and quotes a line of J. L. Austin's.)