Product of oxidation of alkanes
Potassium permanganate, $\ce{KMnO4}$, is the most common and probably the most applicable oxidizing agent discussed in organic chemistry teaching classes. $\ce{KMnO4}$ is a very strong oxidizing agent, and is capable of oxidizing a wide range of organic molecules. Usually, it will oxidize organic compounds to appropriate carboxylic acids, but, the final products can vary on the conditions used. If you googled enough to find reduction potentials of $\ce{KMnO4}$, you may find following conditions, which are the most used reduction conditions of $\ce{KMnO4}$ (Wikipedia):
\begin{align}
\ce{MnO4- + H+ + e- &amp;-&gt; HMnO4^-} &amp; \mathrm{E^o} &amp;= \pu{0.90V}\tag{1}\label{1}\\
\ce{MnO4- + 8H+ + 5e- &amp;-&gt; Mn^2+ + 4H2O} &amp; \mathrm{E^o} &amp;= \pu{1.51V}\tag{2}\label{2}\\ \ce{MnO4- + 2H2O + 3e- &amp;-&gt; MnO2(s) + 4OH-} &amp; \mathrm{E^o} &amp;= \pu{1.69V}\tag{3}\label{3}\\
\ce{MnO4- + 4H+ + 3e- &amp;-&gt; MnO2(s) + 2H2O} &amp; \mathrm{E^o} &amp;=\pu{1.7V}\tag{4}\label{4}
\end{align}
Other manganese containing compounds other than $\ce{KMnO4}$, which can also be used as oxidizing reagents are listed below:
\begin{align}
\ce{MnO2(s) + 4H+ + e- &amp;-&gt; Mn^3+ + 2H2O} &amp; \mathrm{E^o} &amp;= \pu{0.95V}\tag{5}\label{5}\\
\ce{MnO2(s) + 4H+ + 2e- &amp;-&gt; Mn^2+ + 2H2O} &amp; \mathrm{E^o} &amp;= \pu{1.23V}\tag{6}\label{6}\\
\ce{HMnO4- + 3H+ + 2e- &amp;-&gt; MnO2(s) + 2H2O} &amp; \mathrm{E^o} &amp;= \pu{2.09V}\tag{7}\label{7}\\
\end{align}

Yet, as most of the viewers already commented, I also believe $\ce{KMnO4}$ does not oxidize alkanes, except in following situations:

$\ce{KMnO4}$ oxidizes alkane carbon atoms, which contain sufficiently weak $\ce{C-H}$ bonds such as those in benzylic positions ($\ce{C-H}$ bonds in the $\alpha$-positions of substituted aromatic rings). These oxidizable alkyl benzene substituents can be -$\ce{CH3}$, or any $1^\mathrm{o}$-alkyl groups such as -$\ce{CH2CH3}$, or $2^\mathrm{o}$-alkyl groups such as -$\ce{CH(CH3)2}$. All of them will be oxidized to carboxylic acid group, -$\ce{CO2H}$ (See Scheme 1 below): 



It is also important to note that when the benzylic carbon is a $3^\mathrm{o}$-$\ce{C}$ (e.g., corresponding alkyl groups such as $-\ce{C(CH3)3}$ group in tert-butylbenzene, see the example given in RHS of Scheme 1), the oxidation reaction does not happen.  

In addition to benzylic carbons, $\ce{KMnO4}$ also oxidizes weak $\ce{C-C}$ bonds such as $\pi$-bonds in alkenes and alkynes (Scheme 2):



$\ce{KMnO4}$ also oxidizes $\sigma~\ce{C-C}$ bonds such as that in glycol-moiety (e.g., $\ce{HO-C-C-OH}$) and $\ce{C^{\mathrm{sp^2}}-O}$ bonds such as those in phenolic compounds (e.g., it oxidizes phenol to 1,4-benzoquinone, commonly known as para-quinone).

At last, as mentioned above, conditions of the reaction can be adjusted such a way that desired compound can be achied in high yields. For example, see following example (Ref.1):



Note that no benzylic carbon or -$\ce{OCH2}$- was oxidized here. 



Late Addition:

Although tertiary $\ce{C-H}$ bond in isobutane (preferred IUPAC name: 2-methylpropane; $\ce{CH3CH(CH3)CH3}$) is relatively weaker than othe alkane $\ce{C-H}$ bonds, I’m highly skeptical of the statement of “Oxidizing agents such as potassium permanganate readily oxidize a tertiary hydrogen atom to a hydroxyl group, e.g., isobutane is oxidized to t-butanol.” (vide infra). To my knowledge, the literature evidence for that type of oxidation reactions does not exist. Nevertheless, 2-methylpropane (isobutane) can be oxidized to 2-methylprop-2-ol (t-butanol) by reacting supercritical-phase isobutane with air in the presence of a catalyst such as $\ce{Pd/C}$ at high temperature, Instead of using $\ce{KMnO4}$ (Ref.2):


  Abstract: tert-2-Butyl alcohol can be synthesized efficiently on $\ce{SiO2 –TiO2}$ or $\ce{Pd–C}$ catalyst if air is directly introduced to the supercritical-phase isobutane.


tert-Butanol (TBA) is the initial material in methyl tert-butyl ether (MTBE) production and methyl methacrylate (MMA) synthesis.  MTBE is high-octane-number gasoline additive and MMA is a resin material for plastic synthesis (e.g., PMMA or poly-methyl methacrylate). Thus, one would have wondered why scientists did not attempted to synthesize TBA in a such an easy way like using $\ce{KMnO4}$.

However, in a different note, almost exclusive $\ce{C-H}$ bond activation has been observed in the reaction of linear and branched alkanes with $\ce{CeO2+}$ (Ref.3)

Reference:


A. Abiko, J. C Roberts, T. Takemasa, S. Masamune, “$\ce{KMnO4}$ revisited: Oxidation of aldehydes to carboxylic acids in the tert-butyl alcohol - aqueous $\ce{NaH2PO4}$ system,” Tetrahedron Letters 1986, 27(38), 4537-4540 (https://doi.org/10.1016/S0040-4039(00)84997-7)
L. Fan, Y. Nakayama, K. Fujimoto, “Air oxidation of supercritical phase isobutane to tert-butyl alcohol,”  Chem. Commun. 1997, (13), 1179-1180 (DOI:10.1039/A702308A).
A. Gunay, K. H. Theopold, “$\ce{C-H}$ Bond Activations by Metal Oxo Compounds,”  Chem. Rev. 2010, 110(2), 1060–1081 (DOI: 10.1021/cr900269x).