The fourth division side actually reached the final of this competition in 1997, while only Bayern Munich boast more than Werder Bremen's tally of six DFB-Pokal triumphs.
Match preview
Having bounced between the top two divisions of German football between 1997 and 2014, Energie Cottbus have fallen on harder times in recent years, with manager Claus-Dieter Wollitz falling just short of taking them back into 3. Liga after finishing third in Regionaliga Nordost last season.
No team lost fewer games than Energie in their division, but ultimately too many draws cost them the chance to progress to the promotion play-offs for a shot at restoring their third tier status.
Three wins from their last four pre-season friendlies suggest Wollitz's side head into Monday's cup tie with a glimmer of a chance of an upset, though, even if this competition will not represent their main focus this season.
However, this is their first appearance in the competition since losing 3-1 to Bayern three seasons ago, so the home fans are likely to be baying for maximum effort against a side which was only competing two divisions above them last season.
That has changed now, of course, after Werder Bremen secured second spot behind champions Schalke 04 to return to the Bundesliga at the first time of asking, having been relegated for the first time since 1980.
Boss Ole Werner has dramatically improved the club's fortunes since departing Holstein Kiel to take charge of Die Werderaner last November, winning 13 of his 19 games in charge so far, helping his side edge out third-placed Hamburger SV by three points in the end.
The club have brought in seven new players so far this summer as they attempt to avoid being embroiled in another relegation battle, with the £3.6m signing of Jens Stage from FC Copenhagen particularly attracting the eye.
Pre-season has been a mixed bag for Werner and his players, though, with two wins, one draw and two defeats suggesting they will need to guard against any complacency ahead of Monday's trip to Cottbus in a competition which Werder Bremen have plenty of historical pedigree to live up to.
Energie Cottbus pre-season form:
Werder Bremen pre-season form:
Team News
Energie Cottbus will be without midfielders Niclas Erlbeck and Joshua Putze due to injury, while goalkeeper Elias Bethke is doubtful having been struck down by flu.
Wollitz is likely to select the same XI which dispatched Borussia Hildesheim 2-0 in their final pre-season friendly last weekend, with Malcolm Budu and Tim Heike hoping to get on the scoresheet once again.
Werder Bremen, meanwhile, will travel without Dikeni Salifou, Jean Manuel Mbom and Benjamin Goller due to injuries.
Werner's side played two friendlies on the same day last weekend, with the XI which thrashed FC Gronginen 6-1 looking closer to his first team selection.
Should the 34-year-old select the same side, that would mean former competitive debuts for former Derby County left-back Lee Buchanan, central defender Amos Pieper and Mitchell Weiser.
Energie Cottbus possible starting lineup:
Sebald; Milde, Slamer, Borgmann; Eisenhuth, Hofmann, Geisler, Kujovic; Oesterhelweg, Hottmann, Badu
Werder Bremen possible starting lineup:
Pavlenka; Weiser, Pieper, Veljkovic, Friedl, Buchanan; Bittencourt, Schmid, Groß; Fullkrug, Ducksch
We say: Energie Cottbus 0-2 Werder Bremen
We expect a fairly low-tempo affair with this cup tie representing both sides' first competitive matches of the season.
Ultimately, both sides may be content enough with a narrow victory for the visitors, who will be desperate to avoid any upset ahead of their return to the Bundesliga next weekend.