The sum of odd numbers from 1 to some value is nice in that the sum is always the square of the number of odd values.
examples
1 = 1 (= 1^2)
1+3 = 4 (= 2^2)
1+3+5 = 9 (= 3^2)
1+3+5+7 = 16 (= 4^2)
etc.

For the sum of even numbers, we can use the n(n+1)/2 formula. All we need to do is factor out the 2 first.
For example:
2+4+6+8+10+12 = 2(1+2+3+4+5+6)
From here we can use the formula to find the sum of the integers from 1 to 6, which equal (6)(6+1)/2 = 21
So, 2+4+6+8+10+12 = 2(1+2+3+4+5+6) = 2(21) = 42

I hope that helps.

Cheers,
Brent