One has to keep clear that there are two general frameworks where the term "mass" is used. One is the classical framework where $m$ is the inertial mass for $F=ma$, and Newton's laws dominate and one can use Archimedes principle to calculate the mass of alloys. In this system mass is an additive conserved quantity. This is also the low velocity frames, i.e. velocities very small compared with the velocity of light. The classical physics system.
For velocities near the velocity of light one cannot have Galilean transformations (necessary for Newton's mechanics) to go from one frame to another, but Lorenz transformations. One has to use four vectors, $(E,p_x,p_y,p_z)$ and the "length" of this four vector is called the invariant mass characterizing the system. Particles are characterized by this mass $m$ when measured individually, but when in a system, one has to add the four vectors and the sum can be different than the sum of the individual masses comprising the system.
The second frame is the frame of atoms molecules particles, a micro frame because distances are small, governed by quantum mechanics and special relativity.
Protons and neutrons within a nucleus are in a quantum mechanically bound state, i.e a state in a potential well. Their free particle four vectors when falling in the potential well, during the creation of the nucleus, lost energy and momentum by radiation $( α, β, γ )$ and the addition of the four vectors of the nuclei that make up the nucleus has a total mass less than the sum of the masses of the free nuclei.
With the above in mind lets see the question:
Nucleus mass should be equal to sum of mass of protons and neutrons,
Only in the classical physics frame, which is not the frame of protons and neutrons.
but after binding of these particles, its mass is reduced. Why?
Because of special relativity which induces a relationship between masses of systems that have constituents, through the four vectors of each constituent and the law of addition of four vectors.
Due to reduced mass of protons or neurons?
The protons and neutrons in the potential of the nucleus are described by virtual four vectors, and yes, those four vectors have instantaneously different masses , less than the free particle rest mass.
Then what's the purpose of calculated mass?
The measured rest( or invariant) mass of individual protons and neutrons is invariant when the particles are free. The measured rest mass of the composed nucleus is also invariant . The difference of the sum of individual masses to the mass of the nucleus tells how much energy will be needed to get the protons and neutrons free, outside their built up potential well. The potential well of a system of nucleons is built up by the strong force, a spill over of the quantum chormodynamic force between quarks which compose the neutrons and protons.