IMSO 2006 Mathematics · Taiwan Second Round Short Answer Question 18

$a,b,c$ are three positive numbers such that $a+b+c=21$, $a\times a+b\times b+c\times c=147$ and $a\times a\times a+b\times b\times b+c\times c\times c=1029$. What is $3a+2b+c$?