JEE Advance - Mathematics (1996 - No. 18)
For any odd integer $$n$$ $$ \ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3} = ........$$
$$\frac{1}{4}(n+1)^2(2n-1)$$
$$\frac{1}{4}(n-1)^2(2n+1)$$
$$\frac{1}{4}n^2(2n-1)$$
$$\frac{1}{4}(n+1)^2(2n+1)$$
$$\frac{1}{4}n(n+1)(2n-1)$$