小五奧數!!! 急!!!

Find the following numbers without using calculator.
Steps or any formulae are required.
1. 1^3 + 2^3 + 3^3 + 4^3 + 5^5 = ?
Sol
1^3 + 2^3 + 3^3 + 4^3 + 5^5
=(1^3 + 2^3 + 3^3 + 4^3 )+ 5^5
=[4*5/2]^2+5^5
=100+3125
=3225

2. 1^3 + 2^3 + 3^3 + 4^3 + ....+ 53^3 + 54^3 + 55^3 = ?
Sol
1^3 + 2^3 + 3^3 + 4^3 + ....+ 53^3 + 54^3 + 55^3
=[55*(55+1)/2]^2
=1540^2
=2371600




2011-03-20 21:28:18 補充：
1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

By n^3=1/4(n^2)(n+1)^2

1.) 1^3 + 2^3 + 3^3 + 4^3 + 5^5
=1/4(4^2)(4+1)^2+5^5
=100+3125
=3225

2.) 1^3 + 2^3 + 3^3 + 4^3 + ....+ 53^3 + 54^3 + 55^3
=1/4(55^2)(55+1)^2
=1/4(3025)(3136)
=(3025)(784)
=2371600