Copyright 2007 by Rainer Typke.
Volume 2 of the Crossnumber Book contains a description of how this puzzle was created.
Across:
A: A square number.
C: If one adds the average value of E across's digits to C across, the result equals B down divided by C across.
E: A cubic number.
G: A palindrome whose digit sum equals F down.
H: A square number.
Down:
A: Half of the reverse of H across.
B: G across minus C down.
C: All digits are the same.
D: To get D down, add F down's digit product and F-down's digit sum and multiply the result with F down.
F: This cubic number equals the digit sum of B down.