A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to a base category
C
\mathcal {C}
behave like operads in
C
\mathcal {C}
. In this note we show that every cubical Feynman category is Koszul. The upshot is an explicit, minimal cofibrant resolution of any cubical Feynman category, which can be used to model
∞
\infty
versions of generalizations of operads for both graph based and non-graph based examples.