Question 17
An odometer displays the total kilometres a car has travelled. Leonard drives for a positive integer number of hours at average speed $55\,\mathrm{km/h}$. The reading changes from $\overline{abc}$ to $\overline{cba}$. Given $a\ge1$ and $a+b+c\le7$, find $a^3+b^3+c^3$.