If the entire part of the iceberg protruding above the surface of the water is blown up, will the remaining part sink? Why?

Two forces act on the iceberg: the force of gravity Ft directed vertically downward, and the buoyancy force of Archimedes Farch directed vertically upward.
The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.
The buoyancy force of Archimedes is determined by the formula: Farch = ρ * g * V. Where ρ is the density of the liquid in which the body is immersed, g is the acceleration of gravity, V is the volume of the immersed part of the body in the liquid.
These two forces balance each other. When the part of the iceberg that is above the water explodes, the mass of the entire iceberg will decrease, which means that the force of gravity will decrease. Under the action of the buoyant force of Archimedes, the iceberg will rise up, until again the force of gravity is balanced by the force of Archimedes. When the iceberg rises, the volume of the underwater part of the iceberg will decrease, which means that the buoyancy force will also decrease. The iceberg will continue to swim, only its underwater part will decrease.