Ekta Seth from India has managed to find the solution to this problem:

Total no. of black tiles required is $106$. Reason:

• $315 =21\times15$
• Diagonal of the square= $6 \times$ sq.root of $2$. So each side must be greater than $9$.
• Since area of the rec.is $315$, so length and breadth have to be integers.
• Thus border of the rec. has $68$ tiles.
• Inside pattern require $38$ tiles.
• Total=$106$ tiles.