# value of series 2^3+4^3+6^3+........+20^3

#### debos

##### New member
if 1^3+2^3+3^3+4^3................+10^3=3025,then find the value of series 2^3+4^3+6^3+........+20^3.

#### MarkFL

##### Super Moderator
Staff member
What happens if you factor out $$2^3$$ from the second sum?

#### debos

##### New member
What happens if you factor out $$2^3$$ from the second sum?

#### MarkFL

##### Super Moderator
Staff member
The second sum is of the form:

$$\displaystyle S=\sum_{k=1}^{10}\left((2k)^3\right)$$

If we factor, as I suggested, we get:

$$\displaystyle S=2^3\sum_{k=1}^{10}\left(k^3\right)$$

Can you proceed, using the information given in the problem regarding the second factor, which is a sum?

#### debos

##### New member
The second sum is of the form:

$$\displaystyle S=\sum_{k=1}^{10}\left((2k)^3\right)$$

If we factor, as I suggested, we get:

$$\displaystyle S=2^3\sum_{k=1}^{10}\left(k^3\right)$$

Can you proceed, using the information given in the problem regarding the second factor, which is a sum?
Yes, clear now. Thank you.