(1) 1+2=3
(2) 4+5+6=7+8
(3) 9+10+11+12=13+14+15
(4) 16+17+18+19+20=21+22+23+24
-
-
-
.......upto infinity.

Consecutive Square numbers
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(1) 3²+4²=5²
(2) 10²+11²+12²=13²+14²

sum of consecutive cubes
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[1] 1³+2³=(1+2)²=3³
[2] 1³+2³+3³=(1+2+3)²=6²
[3] 1³+2³+3³+4³=(1+2+3+4)²=10²

sum of Consecutive odd numbers
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[1] 1+3=4=2²
[2] 1+3+5=9=3²
[3] 1+3+5+7=16=4²
1+3+5+7+----------n=n²
(n is the number of terms)