The Easter Road side are attempting to reach their third final in four years when they take on Falkirk at Hampden on Saturday.
But to give themselves an opportunity of winning the trophy for the first time in 113 years, Hibs will have to beat their opponents for the first time this season.
The Bairns have recorded two 1-0 wins this term, while the teams shared a six-goal thriller back in January when Falkirk came back from 3-1 down with a storming second-half display.
Hibs, of course, needed extra time after an amazing comeback of their own against the same opponents at the semi-final stage two years ago, when they recovered from a 3-0 half-time deficit to eventually reach the 2013 final with a Leigh Griffiths winner.
However, after Sunday’s Edinburgh derby victory over Hearts – another team Hibs had not beaten until the weekend – Stubbs is optimistic his players can break another unwanted record.
He said: “Hopefully we can put two stats right in the space of two games, because we hadn’t beaten Hearts before Sunday. It’s the same with Falkirk this weekend. It’s different because of the circumstances of the game. It’s about playing at Hampden, where some players won’t have played before.
“I’m sure we’ll have a huge crowd that will follow us there. And it will be about performing on the day and making sure we can try and get ourselves into the next round and a Scottish Cup final.
“I think we have performed OK against them [Falkirk], but I’m very aware that it will be a really difficult game, one where we’ll need to be at our best.There’s obviously a lot at stake – the chance to get to the final of the most prestigious cup competition in Scotland. It’s a huge carrot dangling in front of us.”
One player who could be key to Hibs’ hopes is top scorer Jason Cummings, who took his tally for the season to 17 with the first-half opener against Hearts.
Stubbs admits the 19-year-old is still a raw talent, with much to learn, but has hailed the former Hearts trainee’s burgeoning self-belief.
He added: “We’re always on to Jason because his goalscoring exploits aren’t in question. But he’s got a lot to learn in terms of the game and where he should be, and taking chances and gambling, and hopefully that will all come to him.
“But I think his biggest asset is he’s never going to want for confidence.”
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