According to Bloomberg [bloomberg.com], Apple could owe in excess of $8 billion in back taxes after the conclusion of a European Commission investigation into its Irish tax dodges.
Apple has agreed to pay Italy $348 million for illegally shifting income from Italy (taxable at 12.5%) to Ireland (taxable at 2.5%) over 2008-2013. Bloomberg extends this to the rest of Europe and estimates Apple may end up owing $8 billion in back taxes [appleinsider.com]. While Bloomberg is likely hyping exaggerated numbers to attract readers, Apple wouldn't have a problem paying $8 billion. Apple has about $181 billion in foreign profits laying around. It would cost Apple around $59 billion in U.S. income tax to transfer the money to the U.S.
Google, Amazon, and some other companies are being investigated for similar dealings, and arrangements in Belgium are also being looked into [appleinsider.com].