15. How many of these four expressions are perfect squares?
$$
1^{3}+2^{3} \quad 1^{3}+2^{3}+3^{3} \quad 1^{3}+2^{3}+3^{3}+4^{3} \quad 1^{3}+2^{3}+3^{3}+4^{3}+5^{3}
$$

A 0
B 1
C 2
D 3
E 4
15. E All four expressions are perfect squares: $1^{3}+2^{3}=1+8=9=3^{2}$;
$$
\begin{array}{l}
1^{3}+2^{3}+3^{3}=1+8+27=36=6^{2} ; 1^{3}+2^{3}+3^{3}+4^{3}=1+8+27+64=100 \\
=10^{2} ; 1^{3}+2^{3}+3^{3}+4^{3}+5^{3}=1+8+27+64+125=225=15^{2} .
\end{array}
$$
(It is not a coincidence that all four expressions are squares: the sum of the cubes of the first $n$ integers is equal to the square of the sum of the first $n$ integers for all positive integers n. For example: $1^{3}=1^{2} ; 1^{3}+2^{3}=(1+2)^{2}$; $1^{3}+2^{3}+3^{3}=(1+2+3)^{2} ; 1^{3}+2^{3}+3^{3}+4^{3}=(1+2+3+4)^{2}$ etc. $)$