The general form of a cubic polynomial function is f(x)=ax^3+bx^2+cx+d. Recall that a "polynomial of degree n" is, by definition, the sum of all non-negative integral powers of x (meaning with integer exponents), having "greatest" degree, n, and all coefficients real.
Now, you are given that each of (1,0),(2,0),(3,0),(0,6)and(-1,25)is a solution of the above noted function. That is a mountain of information. First, the value of constant d is a gift. Next, using said mountain, write two equations of the form 0 = ..., such that the terms comprising the "..." contain only a, b, c and 6 (woops, I slipped!). Having done so, you will likely observe a pretty nifty occurance, should you happen to possess sufficient insight to consider adding these equations, thus constructing yet another in the process.
I am confident that, having arrived at the juncture marked by the smiley above, the rest will just "sorta fizzle all together" (in the words of a really cool dude who answers to the name "Neil Young").
Happy function hunting,