Python: How to make drawn elements snap to grid in pygame

I am experimenting with a Pathfinding project and got stuck while creating a working GUI. I'm using pygame and already created a grid and a feature, which draws cubes when you press (or keep pressing) the mouse-button. However, these cubes just go wherever you click, and do not snap to the grid. I thought about using modulo somehow but I cannot seem to get it to work. Please find the code attached below. The Cube class is what I use for the squares drawn on the screen. Moreover, the drawgrid() function is how I set up my grid. I'd love some help on this, as I've been stuck on this roadblock for three days now.

class Cube:
    def update(self):
        self.cx, self.cy = pygame.mouse.get_pos()
        self.square = pygame.Rect(self.cx, self.cy, 20, 20)

    def draw(self):
        click = pygame.mouse.get_pressed()
        if click[0]:  # evaluate left button
            pygame.draw.rect(screen, (255, 255, 255), self.square)

Other drawgrid() function:

def drawgrid(w, rows, surface):
    sizebtwn = w // rows  # Distance between Lines
    x = 0
    y = 0
    for i in range(rows):
        x = x + sizebtwn
        y = y + sizebtwn
        pygame.draw.line(surface, (255, 255, 255), (x, 0), (x, w))
        pygame.draw.line(surface, (255, 255, 255), (0, y), (w, y))

You have to align the position to the grids size. Use the floor division operator (//) to divide the coordinates by the size of a cell and compute the integral index in the grid:

x, y = pygame.mouse.get_pos()

ix = x // sizebtwn
iy = y // sizebtwn

Multiply the result by the size of a cell to compute the coordinate:

self.cx, self.cy = ix * sizebtwn, iy * sizebtwn

Minimal example:

import pygame
pygame.init()

screen = pygame.display.set_mode((200, 200))
clock = pygame.time.Clock()

def drawgrid(w, rows, surface):
    sizebtwn = w // rows 
    for i in range(0, w, sizebtwn):
        x, y = i, i
        pygame.draw.line(surface, (255, 255, 255), (x, 0), (x, w))
        pygame.draw.line(surface, (255, 255, 255), (0, y), (w, y))

class Cube:
    def update(self, sizebtwn):
        x, y = pygame.mouse.get_pos()
        ix = x // sizebtwn
        iy = y // sizebtwn
        self.cx, self.cy = ix * sizebtwn, iy * sizebtwn
        self.square = pygame.Rect(self.cx, self.cy, sizebtwn, sizebtwn)
    def draw(self, surface):
        click = pygame.mouse.get_pressed()
        if click[0]:
            pygame.draw.rect(surface, (255, 255, 255), self.square)

cube = Cube()

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    cube.update(screen.get_width() // 10)

    screen.fill(0)
    drawgrid(screen.get_width(), 10, screen)
    cube.draw(screen)
    pygame.display.flip()