A large iceberg melts at the base and not at the top because

When pressure is applied on ice, its melting point decreases. Let us say the ambient temperature is $-5^0\mathrm{C}$  which is below $0^0\mathrm{C}$ at which ice melts under normal atmospheric pressure conditions.

Pressure on ice in glaciers increases with depth of ice. This lowers its melting point. Under normal atmospheric pressure conditions, melting point of ice is $0^0\mathrm{C}$ at the top of glacier, it decreases continuously and is least at the bottom of the glacier. Let us say melting point of ice at the bottom of the glacier is $-5.1^0\mathrm{C}$. Since ambient temperature is $-5^0\mathrm{C}$, temperature of the ice at the bottom of glacier is above its melting point. This means the ice here should be in liquid form. At this time, melting points of the upper layers will be higher than their temperature ($-5^0\mathrm{C}$). Hence those layers will not melt. Hence glaciers start melting at the bottom.