Ferrer, seeded fourth after reaching the French Open final in June, dropped a set for the second match in a row but was otherwise untroubled in his 6-4 6-3 4-6 6-4 victory.
Kukushkin matched his best performance at a Grand Slam by reaching the third round but contributed to his own downfall by committing 66 unforced errors, almost twice as many as Ferrer.
The Spaniard was a semi-finalist at the US Open in 2007 and again last year. His next opponent will be Janko Tipsarevic who beat Jack Sock 3-6 7-6(1) 6-1 6-2.
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