What is the "empirical formula"?

Ordinarily you have to determine the empirical formula experimentally, (that's what $\text{empirical means}$, $\text{experimental}$), and from this empirical formula, the molecular formula is calculated. I will give you a few examples with this order reversed. The molecular formula of hydrogen peroxide is ${H}_{2} {O}_{2}$; its empirical formula is $O H$. The molecular formula of butane is ${C}_{4} {H}_{10}$; its empirical formula is ${C}_{2} {H}_{5.}$ In both instances the empirical formula is the simplest whole number ratio that defines the proportion of the constituent atoms, as required. What are the empirical formulae of ethane, ${C}_{2} {H}_{6}$, hexane, ${C}_{6} {H}_{14}$, octane, ${C}_{8} {H}_{18}$, and ethanol, ${C}_{2} {H}_{5} O H$?