Question 11
An odometer displays the cumulative distance travelled by a vehicle in its lifetime. Leonard drove his car for an integral number of hours at an average speed of $55\text{ km/h}$. At the start, the odometer displayed $\overline{abc}\text{ km}$; at the end it displayed $\overline{cba}\text{ km}$. Given $a\ge1$ and $a+b+c\le7$, find $a^3+b^3+c^3$.