C-F bond lengths of octafluoropropane using Bent's rule
It is very much non-trivial to attempt estimations on a perfluorated alkane using Bent’s rule. In Bent’s rule, one should not only consider the effects of the electronegative substituents on the substituted atom itself, but also onto the next atom. Consider for example the following table taken from Bent’s review article:[1]

\begin{array}{lr}\hline
\text{Compound} &amp; \angle(\ce{R^1-O-R^2}) \\ \hline
\ce{Me-O-Me} &amp; 111^\circ \\
\ce{Me-O-H} &amp; 107{-}109^\circ \\
\ce{H-O-H} &amp; 104.5^\circ \\
\ce{F-O-F} &amp; 103.8^\circ \\ \hline\end{array}

This very nicely corresponds to increasing group (!) electronegativities[2] in the series $\ce{Me} &gt; \ce{H} &gt; \ce{F}$. $\ce{CF3}$ should have a higher electronegativity than both $\ce{Me}$ and $\ce{H}$ (compare the acidities of formic acid, acetic acid and trifluoroacetic acid). Yet $\angle(\ce{C-O-C}) = 120^\circ$ in $\ce{F3C-O-CF3}$.[3] This corresponds to a higher $\mathrm s$ contribution than for the previous groups indicating other, more important contributions (here the anomeric effect of oxygen acting on the $\ce{CF3}$ group).[4]

Luckily, there are no such secondary effects in perfluoropropane. However, if you want to estimate all bond lengths compared to propane or 2,2-difluoropropane, these must be considered. Specifically, going from propane to 2,2-difluoropropane should not only reduce the $\ce{C-C}$ bond lengths due to increased $\mathrm s$ contribution but also due to partial double bond character due to a gauche-type effect which can be rationalised in Lewis formalism by the following resonance structure:

$$\ce{H-C-C-F &lt;-&gt; \overset{+}{H}\bond{...}C=C\bond{...}\overset{-}{F}}$$

Of course, the partial $\ce{C-C}$ double bond and the less-than-single $\ce{C-F}$ bonds also mess with the observed bond angles in 2,2-difluoropropane; they don’t only influence bond lengths.



So to attempt an estimation of the differences in bond length of the two $\ce{C-F}$ bonds in perfluoropropane, we would need to know how the group electronegativites of the $\ce{CF3}$ and $\ce{C2F5}$ groups compare to the electronegativity of fluorine and to each other. I don’t see any simple way to do this.

Mack et al. have published gas phase structures of 2,2-difluoropropane and perfluoropropane. These are their results (all values in picometres):[5]

\begin{array}{lcc}\hline
\text{compound} &amp; d(\ce{C-C}) &amp; d(\ce{F2RC-F}) &amp; d(\ce{R2FC-F}) \\ \hline
\ce{Me2CF2} &amp; 151.2 &amp; \text{–/–} &amp; 137.0 \\
\ce{(CF3)2CF2} &amp; 154.6 &amp; 132 &amp; 134 \\ 
\ce{Me2CH2} &amp; 153.1 &amp; \text{–/–} &amp; \text{–/–} \\ \hline \end{array}

As you can see, the experimental values just confirm your prediction of the central $\ce{CF2}$ having longer bond lengths than the terminal $\ce{CF3}$ groups. As expected, all $\ce{C-F}$ bonds in perfluoropropane are shorter than the bond lengths of 2,2-difluoropropane. And the $\ce{C-C}$ bond lengths increase from 2,2-difluoropropane to propane to perfluoropropane.

The conclusion is that indeed $\ce{CF3}$ is slightly less electronegative than fluorine, but the effect seems minimal.

References and Notes:

[1]: H. A. Bent, Chem. Rev. 1961, 61, 275–311. DOI: 10.1021/cr60211a005.

[2]: Bent explicitly considers group electronegativities. Only by that is the group electronegativity of a methyl group lower than the electronegativity of hydrogen.

[3]: A. H. Lowrey, C. George, P. D'Antanio, J. Karle, J. Mol. Struct. 1980, 63, 243–248. DOI: 10.1016/0022-2860(80)80330-9.

[4]: F. R. Leroux, B. Manteau, J.-P. Vors, S. Pazenok, Beilstein J. Org. Chem. 2008, 4, 13. DOI: 10.3762/bjoc.4.13.

[5]: H.-G. Mack, M. Dakkouri, H. Oberhammer, J. Phys. Chem. 1991, 95, 3136–3138. DOI: 10.1021/j100161a034.