three terms

$a=second~term$

$d=common~difference$

So the terms are $a-d,a$ and $a+d$ . Then

$a-d+a+a+d=36$

$3a=36$

$a=12$

and

$(a-d)^2+a^2+(a+d)^2=504$

$(12-d)+12^2+(12+d)^2=504$

$144-24d+d^2+144+144+24d+d^2=504$

$2d^2=72$

$d^2=36$

$d=\pm 6$

So the numbers are $6,12$ and $18$ . The sum of their cubes is $6^3+12^3+18^3=\boxed{7776}$