The sum of $\left(5^3+6^3+... 15^3\right)$ is equal to:

14,300

5³ + 6³ + .... + 15³ = ( 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + ......... + 15³ ) - ( 1³ + 2³ + 3³ + 4³ )

Sum of n natural numbers = \(\frac{ n² ( n + 1 )²}{4}\)

= \(\frac{ 15² ( 15 + 1 )²}{4}\) - \(\frac{ 4² ( 4 + 1 )²}{4}\)

= \(\frac{ 15² ( 16 )²}{4}\) - \(\frac{ 4² ( 5 )²}{4}\)

= \(\frac{ 57600}{4}\) - \(\frac{ 400}{4}\)

= 14400 - 100

= 14300

The correct answer is Option (3) →14,300