Motivated by a problem in additive Ramsey theory, we extend Todorčević's partitions of three‐dimensional combinatorial cubes to handle additional three‐dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for every Abelian group G of size ℵ2, there exists a coloring c:G→Z$c:G\rightarrow \mathbb {Z}$ such that for every uncountable X⊆G$X\subseteq G$ and every integer k, there are three distinct elements x,y,z$x,y,z$ of X such that c(x+y+z)=k$c(x+y+z)=k$.