Relative energetics of the C3H4 (allene (1) and propyne (2)), C5H4 (penta-1,2,3,4-tetraene (3) and penta-1,3-diyne (4)), and C7H4 (hepta-1,2,3,4,5,6-hexaene (5) and hepta-1,3,5-triyne (6)) cumulene and poly-yne structures were systematically examined using DFT (B3LYP, BLYP, and BP86), MP2, and CCSD(T) theories. The isomer energy separations, DeltaE, were studied with three schemes: standard optimizations and energy determinations (CCSD(T)/cc-pVXZ//MP2/cc-pVTZ), heats of formation predictions via isodesmic and homodesmotic reactions (CCSD(T)/cc-pVTZ//MP2/cc-pVTZ), and BHLYP functional analysis fitted to experimental data. For the C3H4 isomers, DeltaE was determined to be -1.4 and -1.4 kcal/mol for the first two schemes, with the BHLYP functional analysis being fit to the experimental DeltaE of - 1.4 +/- 0.5 kcal/mol. The three schemes yield DeltaE values of -8.8, -10.1, and -11.7 kcal/mol, respectively, for the C5H4 isomers 3 and 4. The C7H4 isomers 5 and 6 are separated by -14.3, -16.3, and -19.7 kcal/mol when the three schemes are applied. The theoretical heats of formations, DeltaH(f), for I and 2 are 45.5 (47.4 +/- 0.3) and 44.1 kcal/mol (46.0 +/- 0.2) at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level, respectively (experimental values in parentheses). At the same level of theory, 3-6 give DeltaH(f)'s of 111.1, 101.1, 171.6, and 155.4 kcal/mol, respectively. Results from BXLYP (X being a variable to describe the amount of HF exchange included) and energy decomposition analyses in conjunction with previous studies lead to the conclusions that gradient-corrected functionals are not properly constructed to handle delocalized cumulenes and that they tend to overstabilize them.