Minimal k

[MM]

Find the smallest natural number k for which
a) [tex]x_{1}^{2}+x_{2}^{2}+\cdots+x_{k}^{2}=2007[/tex] has natural solutions
b)[tex]x_{1}^{3}+x_{2}^{3}+\cdots+x_{k}^{3}=2008[/tex] has integer solutions.