Question

If $1^3+2^3+3^3+\cdots +9^3=2025$ find the value of $(0.11{)}^3+(0.22{)}^3+\cdots (0.99{)}^3$

Answer 1

$(0.11{)}^3+(0.22{)}^3+(0.33{)}^3+\cdots (0.99{)}^3$
$=\left(0.11{)}^3\right\{1^3+2^3+3^3+4^3\cdots 9^3\}$
$=(0.11{)}^3\times 2025$
$=001331\times 2025$
= 2.695