Is it true or false?

It is $\color{#D61F06} \boxed{\text{false}}.$

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$3^{3n+3} - 26n - 27$

The expression is a multiple of $169$ for all natural $n$ , let's prove that.

For $n = 1$ we are asserting that $\Rightarrow 3^6 -53 = 676 = 169 \cdot 4$ is divisible by $169,$ which is evident.

Assume the assertion is true for $n -1, n>1$ . $\text{i.e}$ assume that

$3^{3n} -26n-1 = 169N$

for some integer $N$ . Then

$\Rightarrow 3^{3n+3} - 26n - 27 = 27 \cdot 3^{3n} -26n -27 = 27(3^{3n} -26n-1) +676n$

which reduces to

$27 \cdot 169N +169 \cdot 4n$

which is divisible by $169.$