Beam loading formula from machinery handbook

That's a cantilevered beam with uniform loading.
The 2nd formula is correct. I've checked 2 of my books.

Looks like different definitions for "w".
In one case (wL^4), w is load per unit length. In the other (wL^3) , w is total load.

As the saying goes: Who ya going to call: Marks Handbook or a private web page and some posters?
Next: I hope you can distinguish between 2nd moment, initialized as 9th letter of the alphabet, upper case I and length, initialized as 12th letter, lower case l . But I think you can.
Last, I hope you are accounting for uniformly distributed load vs. point load - which accounts for a factor of 3/8 in deflection, but I think you are.
That leaves the one definition that you are probably forgetting. A uniform load, which is often given as load per unit length (along the cantilever) versus a uniform load totaled over the whole length. The difference introduces a factor of l
Brian W