(2n+1)²-1²=(2n+1+1)(2n+1-1)=2n(2n+2)=4n(n+1)n和n+1是连续两个整数，所以是一奇一偶所以相乘是偶数，即是2的倍数所以4n(n+1)是2×4=8的倍数所以(2n+1)²-1能被8整除
