Sum of the cubes of first 25 natural numbers = $\left[\dfrac{n × (n + 1)}{2}\right]^{2}$
= $\left[\dfrac{25 × (25 + 1)}{2}\right]^{2}$
= $\left[\dfrac{25 × 26}{2}\right]^{2}$
= $(25 × 13)^{2}$
= $325^{2}$
= 105625