Don't Substitute!

$1 + a + 2b + 3c + 2ab + 3ac + 6bc + 6abc$

Well lets make a new letter named $d$ which is equal to $222$ , So it means that:

$a = 4d$

$b = 3d$

$c = 2d$

Now simplifying the above expression using these codes will make it:

$1 + 4d + 2(3d) + 3(2d) + 2(4d)(3d) + 3(4d)(2d) + 6(4d)(3d)(2d)$

$1 + 4d + 6d + 6d + 24d^2 + 24d^2 + 36d^2 + 144d^3$

$1 + 16d + 84d^2 + 144d^3$

Now we can simply substitute the value of d into this equation:

$1 + 16d + 84d^2 + 144d^3$

which can be factorized into:

$(4d +1)(6d +1)^2$

Now we can substitute $222$ into the expression:

$(4(222) +1)(6(222) +1)^2$

Which is equal to

$=1579654321$

$1+a+2b+3c+2ab+3ac+6bc+6abc$

$=(a+1)(2b+1)(3c+1)=(888+1)(2*666+1)(3*444+1)$

$=889*1333*1333=\boxed{1579654321}$