The 32-year-old, yet to drop a set in four rounds, dazzled the crowd with his artistry, making the game look ludicrously easy against the 22nd best player in the world.
All eyes have been on defending champion Andy Murray's regal progress through the draw so far this year but Federer again issued a reminder that, when his game is flowing on a grass court there are few better sights in world sport.
Eyeing a record eighth Wimbledon title, the maestro has yet to drop a set or a service game in his most impressive route to the quarter-finals since 2004.
Robredo never stood a chance as Federer avenged a humiliating US Open defeat against the Spaniard last year.
"I feel physically in tip top shape," Federer, who now faces an all-Swiss quarter-final against Davis Cup team-mate Stanislas Wawrinka, said.
"I've been in control throughout almost all the matches."
"Hopefully our football team can beat Argentina later and it will be amazing to play Stan in the quarter-finals here because things like that don't happen too often in Swiss sport."
While Federer is facing an unusually busy schedule at Wimbledon because of weather interruptions, Wawrinka will be playing a third match in three days on Wednesday.
The fifth seed beat Feliciano Lopez 7-6(5) 7-6(7) 6-3 without any major alarms although the match ended with the players in a heated debate at the net.
Big-serving Milos Raonic celebrated Canada Day by becoming the first man from his country to reach the quarter-finals at Wimbledon in the professional era, beating Japan's 10th seed Kei Nishikori 4-6 6-1 7-6(4) 6-3.
Raonic will face Nick Kyrgios for a place in the semi-finals after the Australian wild card's heroics against world No.1 Rafael Nadal.
- Sports & Recreation
- Tommy Robredo
- Stanislas Wawrinka