1 + 8 + 27 +...........

Sum of cubes of n consecutive natural number is given by (n(n+1)/2)^2. Therefore,answer=3025.

Some very useful relations: $\sum_{i=1}^n i^3=\left(\sum_{i=1}^n i\right)^2\quad\color{grey}{\text{and}}\quad\sum_{i=1}^n i=\dfrac{n(n+1)}2$ Therefore: $\begin{aligned} \sum_{i=1}^{10} i^3&=\left(\sum_{i=1}^{10} i\right)^2 \\ &=\left(\dfrac{10(10+1)}{2}\right)^2\\ &=55^2\\ &=\boxed{3025} \end{aligned}$

Hello,

as 1+8+27+......................+1000, it is actually n^(3) for n=[1,10].....

1 = 1x1x1

8 = 2x2x2

27 = 3x3x3

64 = 4x4x4

125 = 5x5x5

216 = 6x6x6

343 = 7x7x7

512 = 8x8x8

729 = 9x9x9

1000 = 10x10x10

Therefore,by adding 1+8+27+64+125+216+343+512+729+1000=3025....

Add them, its just of $10$ numbers or input $\displaystyle \sum_{n = 1}^{10} n^3 = \color{#69047E}{\boxed{3025}}$ .

Sum of Cubes of consecutive no = to consecutive nos sum's square. For Eg :- 1^3 + 2^3 + 3^3 = (1+2+3)^2

formula for um of cubes is (n(n+1)/2)^2. so ans =3025

(10 11) (10*11)/4=3025

1,8and 27 are cubes of 1 2 3 1000 is cube of 10 so add the cubes of numbers 1-10 that is : 1 8 27 64 125 216 343 512 729 1000 to get answer 3025

simple method

1^3 +2^3 +3^3 +.........+n^3 = ((n(n+1)/2))^2 Thus n=10 implies, 10*11/2 * 10 *11/2 = 3025

$1^3 +2^3+...+n^3=(1+2+3+...+n)^2$ $n=10 \Rightarrow 1^3+2^3+...+10^3=( \frac{10\cdot 11}{2})^2=\boxed{3025}$