No zero occurs in this puzzle.
Across: A: a cubic number whose digit sum equals that of C down.
E: G across divided by F across.
F: a square number.
G: A across + F across
Down: A: A palindrome.
B: all digits are the same. Also, this number has the same digit sum as G across.
C: A prime number.
D: A multiple of the digit sum of C down. Also, the digit sum of D down is a square number.