Three numbers 1^3, 2^3, 3^3 are added: 1 + 8 + 27 = 36 = 6^2. It is a known fact that 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2. Using this, find 1^3 + 2^3 + 3^3 + 4^3.

Question

Accepted Answer

100. 1 + 2 + 3 + 4 = 10, so the sum of cubes = 10^2 = 100. Check: 1 + 8 + 27 + 64 = 100.

Three numbers $1^{3}, 2^{3}, 3^{3}$ are added: $1 + 8 + 27 = 36 = 6^{2}$ .
It is a known fact that $1^{3} + 2^{3} + ... + n^{3} = (1 + 2 + ... + n)^{2}$ . Using this, find $1^{3} + 2^{3} + 3^{3} + 4^{3}$ .

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More Class 8 Perfect Cubes practice

Three numbers 13,23,33 are added: 1+8+27=36=62.It is a known fact that 13+23+...+n3=(1+2+...+n)2. Using this, find 13+23+33+43.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Perfect Cubes practice

Three numbers $1^{3}, 2^{3}, 3^{3}$ are added: $1 + 8 + 27 = 36 = 6^{2}$ .
It is a known fact that $1^{3} + 2^{3} + ... + n^{3} = (1 + 2 + ... + n)^{2}$ . Using this, find $1^{3} + 2^{3} + 3^{3} + 4^{3}$ .