求2的3次方+4的3次方+6的3次方......30的3次方的值

1^3+2^3+3^3+……+n^3=[n(n+1)/2]^2
n=15

1^3+2^3+..+15^3=[15*16/2]^2=14400
2^3+4^3+6^3+......+30^3
=2^3*(1^3+2^3+3^3+...+15^3)
=8*14400=115200

补充：
1^3+2^3+3^3+……+n^3=[n(n+1)/2]^2

(n+1)^4-n^4=[(n+1)^2+n^2][(n+1)^2-n^2]
=(2n^2+2n+1)(2n+1)
=4n^3+6n^2+4n+1

2^4-1^4=4*1^3+6*1^2+4*1+1
3^4-2^4=4*2^3+6*2^2+4*2+1
4^4-3^4=4*3^3+6*3^2+4*3+1
......
(n+1)^4-n^4=4*n^3+6*n^2+4*n+1

各式相加有
(n+1)^4-1=4*(1^3+2^3+3^3...+n^3)+6*(1^2+2^2+...+n^2)+4*(1+2+3+...+n)+n

4*(1^3+2^3+3^3+...+n^3)=(n+1)^4-1+6*[n(n+1)(2n+1)/6]+4*[(1+n)n/2]+n
=[n(n+1)]^2

1^3+2^3+...+n^3=[n(n+1)/2]^2

8
64
216
512
1000
1728
2744
4096
5832
8000
10648
13824
17576
21952
27000

死算的 哈哈 115200

2^3+4^3+6^3+......30^3
=2^3+2^3*2^3+2^3*3^3+.....2^3*15^3
=2^3(1+2^3+3^3+4^3+.....15^3)
=115200