The missing number is $\boxed{1023}$.
The numbers in the sequence are the sum of the squares of the first $n$ natural numbers, where $n$ is the position of the number in the sequence. For example, the first number in the sequence is $1$, which is the square of $1$. The second number in the sequence is $4$, which is the square of $2$. The third number in the sequence is $9$, which is the square of $3$. And so on.
The tenth number in the sequence is the sum of the squares of the first $10$ natural numbers, which is $1023$.
Here is a table of the first few numbers in the sequence:
Number | Sum of the squares of the first $n$ natural numbers ------- | -------- 1 | $1$ 2 | $4$ 3 | $9$ 4 | $16$ 5 | $25$ 6 | $36$ 7 | $49$ 8 | $64$ 9 | $81$ 10 | $1023$