Cole's favourite memory with his close friend came against South Africa in England's World Cup semi-final defeat last year, after the duo managed to hold off the power of the world champions' scrum.
"The 2023 semi-final when I came off and he had come off just before me, we shared a hug and said 'well done'," he recalled. "After what happened in previous World Cups that was my favourite moment on the field together."
Uncapped Sale Sharks prop Asher Opoku-Fordjour was called up to the England squad to replace Marler, with Saturday's Test against Australia the first potential opportunity for the highly rated 20-year-old to feature.
"He's obviously been playing fantastically well in the Premiership for Sale," added Cole.
"But it's not about replacing like-for-like, it's not about him replacing Marler.
"It's about bringing your own personality. It's not trying to be someone else."