A hat-trick from Alvaro Negredo, two from Edin Dzeko and one from Yaya Toure all but secured City's place in the final on March 2, while piling more pressure on West Ham manager Sam Allardyce, who is now 1/5 to be the next Premier League manager to lose his job.
Sky Bet's Sandro Di Michele said: "Allardyce has seen his side beaten by an aggregate of 11 goals to nil over the last few days and, whatever the West Ham board say, his position has to be under threat."
City are now clear favourites for the Capital One Cup with their final opponents unclear after Sunderland beat Manchester United 2-1 in the first leg of their semi. United remain odds-on to qualify at 2/5 and are 12/5 to lift the trophy, with Sunderland on offer at 9/1.
"There's work to do for David Moyes and Manchester United but Sunderland struggle for goals on the road and we still expect United to progress," added Di Michele.
"But if City keep up the form they're in now it might not matter who they face come March and they're very strong in the market."