How many of these four expressions are perfect squares?  $$1^{3}+2^{3}$$~ ~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}$$~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}+4^{3}$$~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}+4^{3}+5^{3}$$ 
Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
All four expressions are perfect squares:  $$1^{3} + 2^{3} = 1 + 8 = 9 = 3^{2}$$;  $$1^{3}+2^{3}+3^{3}=1+8+27=36=6^{2}$$;  $$1^{3}+2^{3}+3^{3}+4^{3}=1+8+27+64=100=10^{2}$$;  $$1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} = 1 + 8 + 27 + 64 + 125 = 225 = 15^{2}$$. 