The exclusive online preview appears in the using a widget from music streaming website , which also includes links to purchase tracks online.
The Guardian plans to promote the offer on the home page of its website and in the print editions of its newspaper tomorrow.
Cocker's second solo album, which is due for release next Monday through Rough Trade records, has received initial glowing reviews. Cocker is presently touring around the UK to promote the new album.
Depeche Mode followed a similar route for their comeback effort last month by signing an exclusive ad funded deal with NME.com to stream 'Sounds of the Universe' a week before its release.
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