You're correct that the large numbers are very hard to factor!

In fact, the trick here is to use algebra and factoring a little more. Applying difference of cubes you should get $(1200+1)(1200^2 - 1200 + 1)$. Now, however, note we can write $$1200^2 - 1200 + 1 = 1200^2 + 2\cdot 1200 + 1 - 3\cdot 1200.$$Now we can apply difference of squares here.

Hope this helps!