Squares of 5 consecutive integers

A=10, B=11, C=12, D=13, E=14.
10x10 + 11x11 + 12x12 = 13x13 + 14x14

Do you know the secret of the nature? Look this:
1). 3x3 + 4x4 = 5x5
2). 10x10 + 11x11 + 12x12 = 13x13 + 14x14
3). 21x21 + 22x22 + 23x23 + 24x24 = 25x25 + 26x26 + 27x27
4). 36x36 + 37x37 + 38x38 + 39x39 + 40x40 = 41x41 + 42x42 + 43x43 + 44x44
5). 55x55 + 56x56 + 57x57 + 58x58 + 59x59 + 60x60 = 61x61 + 62x62 + 63x63 + 64x64 + 65x65
Notce the items on the left side of the equal sign, they have the attribute 2N(N+1). Is it amazing?