If I have produced 1 mL of and ester and the density is 1.05 g/mL, what is the mass?

The question should be: "If I have produced 1 mL of an ester and the density is 1.05 g/mL, what is the mass?"

Density = Mass / Volume
Then, Mass of the ester = Density × Volume = (1.05 g/mL) × (1 mL) = 1.05 g

The density - by definition and by the units - tells you that the compound has mass = 1.05g for every mL
The mass of 1mL is 1.05g That is the answer.

In strict terms , taking significant figures into account , the answer is 1g

Seriously? You can do this one in your head. Think about it.

http://www.wolframalpha.com/

http://www.wolframalpha.com/examples/Chemistry.html

Remember the equation
Density = mass / volume
Hence
mass = density x volume
mass(g) = 1.05 g/mL X 1 mL
mass = 1.05 g