Explanation

 1 + 2 + 3 + ... + n = 15  

This is an arithmetic series. Use the formula:

n(n + 1)/2 = 15  

→ Multiply both sides by 2:  

n(n + 1) = 30  

Try n = 5:  

5(6) = 30 

So, n = 5

Now calculate:  

1³ + 2³ + 3³ + ... + n³  

Use formula:  

[n(n + 1)/2]² = [5×6/2]² = (15)² = 225